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Mathematical function whose derivative exists
continuous function; there exist functions that are differentiable but not continuously differentiable (an example is given in the section Differentiability classes)
Differentiable_function
Degree of differentiability of a function or map
This should be distinguished from complex differentiability: a complex function that is complex differentiable on an open subset of C {\displaystyle \mathbb
Smoothness
Function defined by multiple sub-functions
that the value of the right sub-function is used in this position. For a piecewise-defined function to be differentiable on a given interval in its domain
Piecewise_function
Concept in real analysis
{\displaystyle D} be the set of points at which a real function is differentiable, but not continuously differentiable. Let f : R → R {\displaystyle f:\mathbb {R}
Continuously differentiable function of a single real variable
Continuously_differentiable_function_of_a_single_real_variable
Function that is continuous everywhere but differentiable nowhere
Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere
Weierstrass_function
Complex-differentiable (mathematical) function
mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each
Holomorphic_function
On converting relations to functions of several real variables
Allendoerfer, Carl B. (1974). "Theorems about Differentiable Functions". Calculus of Several Variables and Differentiable Manifolds. New York: Macmillan. pp. 54–88
Implicit_function_theorem
Theorem in mathematics
versions of the inverse function theorem for holomorphic functions, for differentiable maps between manifolds, for differentiable functions between Banach spaces
Inverse_function_theorem
Differentiable function whose derivative is not Riemann integrable
properties: V is differentiable everywhere The derivative V ′ is bounded everywhere The derivative is not Riemann-integrable. The function is defined by
Volterra's_function
Manifold upon which it is possible to perform calculus
another is differentiable), then computations done in one chart are valid in any other differentiable chart. In formal terms, a differentiable manifold
Differentiable_manifold
Mathematical operation in calculus
can be found by similar methods. Let F {\displaystyle F} be a differentiable function of two variables, and suppose that an equation F ( x , y ) = f
Implicit_differentiation
Mathematical functions which are smooth but not analytic
In real analysis, a smooth function is infinitely differentiable at each point in its domain, while a real analytic function is, at each point in its domain
Non-analytic_smooth_function
Instantaneous rate of change (mathematics)
derivatives are the result of differentiating a function repeatedly. Given that f {\displaystyle f} is a differentiable function, the derivative of f {\displaystyle
Derivative
Theorem in real analysis
analysis, Rolle's theorem (or lemma) states that a real-valued differentiable function which attains equal values at two distinct points must have a stationary
Rolle's_theorem
Mathematical process of finding the derivative of a trigonometric function
The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change
Differentiation of trigonometric functions
Differentiation_of_trigonometric_functions
Real function with secant line between points above the graph itself
that interval. If a function is differentiable and convex then it is also continuously differentiable. A differentiable function of one variable is convex
Convex_function
Strong form of uniform continuity
to 1. Lipschitz continuous functions that are everywhere differentiable but not continuously differentiable The function f ( x ) = { x 2 sin ( 1 /
Lipschitz_continuity
Study of rates of change
approximation to a differentiable function near a point. In this sense, differentiation is closely related to the differential. For functions of several variables
Differential_calculus
Property of a mathematical function
zero (note that this indicator function is not left differentiable at zero). If a real-valued, differentiable function f, defined on an interval I of
Semi-differentiability
Formula for the derivative of an inverse function
calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the
Inverse_function_rule
Rules for computing derivatives of functions
{d^{k}}{dx^{k}}}g(x).} Differentiable function – Mathematical function whose derivative exists Differential of a function – Notion in calculus Differentiation of integrals –
Differentiation_rules
Theorem in mathematics
theorem) is a theorem about differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to
Mean_value_theorem
Analyzes the topology of a manifold by studying differentiable functions on that manifold
by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold
Morse_theory
Generalized function whose value is zero everywhere except at zero
delta function is to a differentiable manifold where most of its properties as a distribution can also be exploited because of the differentiable structure
Dirac_delta_function
Point where the derivative of a function is zero or undefined (in certain cases)
Jacobian matrix is not maximal. It extends further to differentiable maps between differentiable manifolds, as the points where the rank of the Jacobian
Critical_point_(mathematics)
Derivative defined on normed spaces
function that is Fréchet differentiable at a point is necessarily continuous there and sums and scalar multiples of Fréchet differentiable functions are
Fréchet_derivative
Mathematical relation consisting of a multi-variable function equal to zero
an implicit function that is differentiable in some small enough neighbourhood of (a, b); in other words, there is a differentiable function f that is defined
Implicit_function
Measure of local oscillation behavior
C_{c}^{1}(\Omega ,\mathbb {R} ^{n})} is the set of continuously differentiable vector functions of compact support contained in Ω {\displaystyle \Omega }
Total_variation
Approximation of a function by a polynomial
Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree k {\textstyle k}
Taylor's_theorem
Multivariate derivative (mathematics)
of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle
Gradient
Type of function in mathematics
complex differentiable at every point of the set. For this reason, in complex analysis the terms analytic function and holomorphic function are often
Analytic_function
Formula in calculus
formula that expresses the derivative of the composition of two differentiable functions z and y in terms of the derivatives of z and y. More precisely
Chain_rule
Branch of mathematics studying functions of a complex variable
holomorphic functions that are the differentiable functions of a complex variable. By contrast with the real case, a holomorphic function is always infinitely
Complex_analysis
Nowhere analytic, infinitely differentiable function
the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by Jaap Fabius (1966). This function satisfies
Fabius_function
Generalization of the concept of directional derivative
redirect targets Differentiable vector-valued functions from Euclidean space – Differentiable function in functional analysis Differentiation in Fréchet spaces
Gateaux_derivative
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f:U\to \mathbb {R} }
Harmonic_function
Counterintuitive mathematical object
Weierstrass function, a function that is continuous everywhere but differentiable nowhere. The sum of a differentiable function and the Weierstrass function is
Pathological_(mathematics)
Differentiable function whose derivative is everywhere injective
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly
Immersion_(mathematics)
Negative of a convex function
a\}} are convex sets. A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically
Concave_function
Matrix of partial derivatives of a vector-valued function
be differentiable for its Jacobian matrix to be defined, since only its first-order partial derivatives are required to exist. If f is differentiable at
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Type of derivative in mathematics
{\displaystyle a} , then f {\displaystyle f} is differentiable at a {\displaystyle a} . If f {\displaystyle f} is differentiable at a point, then the derivative of
Derivative (multivariable calculus)
Derivative_(multivariable_calculus)
Notion in calculus
and differentiable functions f and g, d ( a f + b g ) = a d f + b d g . {\displaystyle d(af+bg)=a\,df+b\,dg.} Product rule: For two differentiable functions
Differential_of_a_function
Evaluates a line integral through a gradient field using the original scalar field
rather than just the real line. If φ : U ⊆ Rn → R is a differentiable function and γ a differentiable curve in U which starts at a point p and ends at a point
Gradient_theorem
Indefinite integral
function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function
Antiderivative
Association of one output to each input
century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized
Function_(mathematics)
Mathematical function with no sudden changes
is also everywhere continuous but nowhere differentiable. The derivative f′(x) of a differentiable function f(x) need not be continuous. If f′(x) is continuous
Continuous_function
Mathematical idealization of the trace left by a moving point
regularity, the function that defines a curve is often supposed to be differentiable, and the curve is then said to be a differentiable curve. A plane
Curve
Method of mathematical differentiation
implemented, at least in part, in the differentiation of almost all differentiable functions, providing that these functions are non-zero. The method is used
Logarithmic_differentiation
Polynomial function of degree 3
values of a function and its derivative at some sampling points, one can interpolate the function with a continuously differentiable function, which is
Cubic_function
Second-order partial differential equation describing motion of mechanical system
the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains
Euler–Lagrange_equation
Method to find local maxima and minima of differentiable functions on open sets
can also be extended to differentiable manifolds. If f : M → R {\displaystyle f:M\to \mathbb {R} } is a differentiable function on a manifold M {\displaystyle
Interior_extremum_theorem
Zero of the derivative of a function
a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally
Stationary_point
Differential equation that is linear with respect to the unknown function
arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable
Linear_differential_equation
Description of continuous random distribution
density function if its cumulative distribution function F(x) is absolutely continuous. In this case: F is almost everywhere differentiable, and its
Probability_density_function
Mathematical transformation
of differentiable manifolds). This definition is equivalent to the modern mathematicians' definition as long as f {\displaystyle f} is differentiable and
Legendre_transformation
Method for finding stationary points of a function
Newton–Raphson) is an iterative method for finding the roots of a differentiable function f {\displaystyle f} , which are solutions to the equation f ( x
Newton's method in optimization
Newton's_method_in_optimization
Mathematical function, denoted exp(x) or e^x
definitions of the exponential function, although of very different nature. The exponential function is the unique differentiable function that equals its derivative
Exponential_function
Mapping which preserves all topological properties of a given space
\theta \right).} The graph of a differentiable function is homeomorphic to the domain of the function. A differentiable parametrization of a curve is a
Homeomorphism
Technique in integral evaluation
requirement that φ be continuously differentiable can be replaced by the weaker assumption that φ be merely differentiable and have a continuous inverse.
Integration_by_substitution
function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function
Glossary_of_calculus
Theorem in analysis
versions of the Wirtinger inequality: Let y be a continuous and differentiable function on the interval [0, L] with average value zero and with y(0) =
Wirtinger's inequality for functions
Wirtinger's_inequality_for_functions
Method in statistics
when the random variable being considered can be defined as a differentiable function of a random variable which is asymptotically Gaussian. More generally
Delta_method
Method of differentiating single-term polynomials
differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the
Power_rule
Objects that generalize functions
is not shared by most other notions of differentiation. If m : U → R is an infinitely differentiable function and T is a distribution on U, then the product
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Mathematical method in calculus
v} to be continuously differentiable. Integration by parts works if u {\displaystyle u} is absolutely continuous and the function designated v ′ {\displaystyle
Integration_by_parts
Calculus of vector-valued functions
are used to replace complicated functions with linear functions that are almost the same. Given a differentiable function f(x, y) with real values, one
Vector_calculus
Continuously differentiable function: differentiable, with continuous derivative. Smooth function: Has derivatives of all orders. Lipschitz function, Holder
List_of_types_of_functions
Largest and smallest value taken by a function at a given point
points on the boundary, and take the greatest (or least) one. For differentiable functions, Fermat's theorem states that local extrema in the interior of
Maximum_and_minimum
Isomorphism of differentiable manifolds
continuously differentiable. Given two differentiable manifolds M {\displaystyle M} and N {\displaystyle N} , a continuously differentiable map f : M →
Diffeomorphism
On when a family of real, continuous functions has a uniformly convergent subsequence
continuous function, as claimed. This completes the proof. The hypotheses of the theorem are satisfied by a uniformly bounded sequence {fn} of differentiable functions
Arzelà–Ascoli_theorem
Mathematical theorem, used in calculus
is differentiable. As f {\displaystyle f} is continuous at any x {\displaystyle x} , F := ∫ 0 x f {\displaystyle F:=\int _{0}^{x}f} is differentiable at
Integral_of_inverse_functions
Operation in differential calculus
differentiable at x = 0, but is symmetrically differentiable there with symmetric derivative 0. For differentiable functions, the symmetric difference quotient does
Symmetric_derivative
Mathematics of real numbers and real functions
on the entire real line but not differentiable anywhere (see Weierstrass's nowhere differentiable continuous function). It is possible to discuss the
Real_analysis
Characteristic property of holomorphic functions
Conversely, if the functions u and v are (real) differentiable at z and satisfy the Cauchy-Riemann equations there, then f is complex-differentiable at z. In this
Cauchy–Riemann_equations
Programming paradigm
Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation
Differentiable_programming
exist functions which are not in any Baire class. Examples: The derivative of any differentiable function is of class 1. An example of a differentiable function
Baire_function
Topological space that locally resembles Euclidean space
additional structure. One important class of manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric
Manifold
Mathematical model of the time dependence of a point in space
equations. If Φ is continuously differentiable the system is called a differentiable dynamical system. The function f is therefore a "smooth" mapping
Dynamical_system
Artificial neural network node function
Continuously differentiable This property is desirable for enabling gradient-based optimization methods (ReLU is not continuously differentiable and has some
Activation_function
Mathematical theorem
fact smooth functions are another valid domain. In terms of the total derivative, the second derivative of a twice-differentiable function f : X → Y {\displaystyle
Symmetry of second derivatives
Symmetry_of_second_derivatives
Point where the curvature of a curve changes sign
the curvature changes its sign. For example, the graph of the differentiable function has an inflection point at (x, f(x)) if and only if its first derivative
Inflection_point
Equivalence class of objects sharing local properties at a point in a topological space
local properties, such as continuity, differentiability etc., so it makes sense to talk about a differentiable or analytic germ, etc. Similarly for subsets:
Germ_(mathematics)
Concept in mathematics
iterative optimization algorithm for finding a local minimum of a differentiable function. It generalizes algorithms such as gradient descent and multiplicative
Mirror_descent
Order-preserving mathematical function
{\displaystyle f} is a monotonic function defined on an interval I {\displaystyle I} , then f {\displaystyle f} is differentiable almost everywhere on I {\displaystyle
Monotonic_function
Mathematical definition of point elasticity
mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output) at point
Elasticity_of_a_function
Theorem in convex analysis
derivative of the maximum of a (not necessarily convex) directionally differentiable function. An extension to more general conditions was proven 1971 by Dimitri
Danskin's_theorem
Real function with finite total variation
chains of inclusions for continuous functions over a closed, bounded interval of the real line: Continuously differentiable ⊆ Lipschitz continuous ⊆ absolutely
Bounded_variation
Concept in complex analysis
variable, when applied to holomorphic functions, antiholomorphic functions or simply differentiable functions on complex domains. These operators permit
Wirtinger_derivatives
Average uncertainty in variable's states
information learned from each event. I(p) is a twice continuously differentiable function of p. Given two independent events, if the first event can yield
Entropy_(information_theory)
Algorithm for finding zeros of functions
Suppose that the function f has a zero at α, i.e., f(α) = 0, and f is differentiable in a neighborhood of α. If f is continuously differentiable and its derivative
Newton's_method
Theorem of convex functions
building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. Given its generality, the inequality appears
Jensen's_inequality
Mathematical function, inverse of an exponential function
of functions pass to their inverses. Thus, as f(x) = bx is a continuous and differentiable function, so is logb y. Roughly, a continuous function is differentiable
Logarithm
Function with a multiplicative scaling behaviour
every maximal continuously differentiable solution of this partial differentiable equation is a positively homogeneous function of degree k, defined on a
Homogeneous_function
Type of infinitesimal in calculus
for some differentiable function Q {\displaystyle Q} in an orthogonal coordinate system (hence Q {\displaystyle Q} is a multivariable function whose variables
Exact_differential
Generalized mathematical function
viewed as a subset of X × Y. When f is a differentiable function between manifolds, the inverse function theorem gives conditions for this to be single-valued
Multivalued_function
Oscillatory error in Fourier series
continuously differentiable periodic function around a jump discontinuity. The N {\textstyle N} th partial Fourier series of the function (formed by summing
Gibbs_phenomenon
Mathematical theorem
Lipschitz continuous, then f is differentiable almost everywhere in U; that is, the points in U at which f is not differentiable form a set of Lebesgue measure
Rademacher's_theorem
Theorem on holomorphic functions
difference between holomorphy and real-differentiability. On the real line, for example, the differentiable function f ( x ) = x 2 {\displaystyle f(x)=x^{2}}
Open mapping theorem (complex analysis)
Open_mapping_theorem_(complex_analysis)
Study of mathematical algorithms for optimization problems
an optimal solution as a function of underlying parameters. For unconstrained problems with twice-differentiable functions, some critical points can
Mathematical_optimization
Function whose composition with the logarithm is convex
X, then it vanishes everywhere in the interior of X. If f is a differentiable function defined on an interval I ⊆ R, then f is logarithmically convex
Logarithmically convex function
Logarithmically_convex_function
DIFFERENTIABLE FUNCTION
DIFFERENTIABLE FUNCTION
Boy/Male
Afghan, Arabic, Muslim, Pashtun
One who can Differentiate; Comely; One who Distinguishes Truth from Falsehood
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, a great functionary.
Biblical
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Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Male
Celtic
, great justiciary, or functionary.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Boy/Male
Irish
From the Latin patricius “â€nobly born.â€â€ The patron saint of Ireland, it is hard to differentiate between fact and myth. What is probably true is that he was born in Britain around 373 AD and was brought to Ireland as a slave at the age of seven, possibly by Niall of the Nine Hostages (read the legend). Forced to guard sheep on the Slemish Mountains in Country Antrim for six years he had a vision urging him to convert his captors. He escaped to France where he trained as a priest before returning to Ireland where he banished the snakes (i.e. paganism) and converted the population to Christianity. Both Patrick and Padraig are very popular names in Ireland.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Boy/Male
Irish
From the Latin patricius “â€nobly born.â€â€ The patron saint of Ireland, it is hard to differentiate between fact and myth. What is probably true is that he was born in Britain around 373 AD and was brought to Ireland as a slave at the age of seven, possibly by Niall of the Nine Hostages (read the legend). Forced to guard sheep on the Slemish Mountains in Country Antrim for six years he had a vision urging him to convert his captors. He escaped to France where he trained as a priest before returning to Ireland where he banished the snakes (i.e. paganism) and converted the population to Christianity. Both Patrick and Padraig are very popular names in Ireland.
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
DIFFERENTIABLE FUNCTION
DIFFERENTIABLE FUNCTION
Boy/Male
English
Lives at the cliffs.
Boy/Male
Arabic, German, Hindu, Indian, Marathi, Muslim, Oriya, Turkish
Ray of Light; Shoot of Grass; Green; Spring Greening; Powerful; Strong
Female
Italian
Italian name DIAMANTE means "diamond."
Boy/Male
Hindu, Indian
The Rising Sun
Boy/Male
Hindu
Lord Murugan
Boy/Male
Indian, Punjabi, Sikh
Pure Victory of the Lord
Girl/Female
Hindu, Indian, Telugu
Tender Flower; (Mentioned by Poets in Poetry); Precious Flower; Goddess Lakshmi; Flower
Male
Greek
(Πτολεμαῖος) Greek name derived from the word polemeios, PTOLEMAIOS means "aggressive, warlike."
Boy/Male
Arabic, Muslim
Star of the State
Boy/Male
Hindu
Laukik
DIFFERENTIABLE FUNCTION
DIFFERENTIABLE FUNCTION
DIFFERENTIABLE FUNCTION
DIFFERENTIABLE FUNCTION
DIFFERENTIABLE FUNCTION
v. t.
To distinguish or mark by a specific difference; to effect a difference in, as regards classification; to develop differential characteristics in; to specialize; to desynonymize.
a.
Of or pertaining to a differential, or to differentials.
n.
One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
n.
An increment, usually an indefinitely small one, which is given to a variable quantity.
n.
A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
v. t.
To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.
pl.
of Differentia
n.
An instrument consisting in part of a differential thermometer. It is used for measuring changes of temperature produced by different conditions of the sky, as when clear or clouded.
adv.
In the way of differentiation.
n.
The eliminant of the n partial differentials of any homogenous function of n variables. See Eliminant.
a.
Relating to differences of motion or leverage; producing effects by such differences; said of mechanism.
n.
A characteristic or essential attribute; a differential.
n.
A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities.
v. i.
To acquire a distinct and separate character.
v. t.
To express the specific difference of; to describe the properties of (a thing) whereby it is differenced from another of the same class; to discriminate.
n.
The operation of finding the primitive function which has a given function for its differential coefficient. See Integral.
a.
Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate.
a.
The integral used in obtaining the area bounded by a curve; hence, the definite integral of the product of any function of one variable into the differential of that variable.
a.
Ready to obey; reverent; differential; also, servilely submissive.