Differential calculus

In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. The derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a d

value that a function (or sequence) approaches as the argument (or index) approaches some value

subfield of calculus

expression of a function as an infinite sum

thumb|300px|The gradient, represented by the blue arrows, denotes the direction of greatest change of a scalar function. The values of the function are represented in greyscale and increase in value from white (low) to dark (high).

differential equation containing one or more functions of one independent variable and its derivatives

point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave to convex, or vice versa

notion in calculus

the matrix of all first-order partial derivatives of a vector-valued function

function defined by a relation of the form 𝑅(𝑥,𝑦)=0, where 𝑅 is a function of several variables and there is a unique 𝑦 that satisfies the relation for every 𝑥

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instantaneous rate of change of the function

mathematical operation

method to find local maxima and minima of differentiable functions on open sets

approximation of a function by its tangent line at a point

ratio of a function's derivative to the function; d(ln|f(x)|)/dx

derivative of a function of several variables with respect to one variable, without the others held constant

differentiation under the integral sign formula

mathematical notation

point on a graph where all derivatives or partial derivatives are zero

mathematical process of finding the derivative of a trigonometric function

book by Isaac Newton

In mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.

derivative of a function with respect to time

algorithms for estimating the derivative of mathematical functions

mathematical notation for differential calculus

set of computer programming techniques to speedily compute derivatives

method of differentiation often used when it is easier to differentiate the logarithm of a function rather than the function itself

method for finding the extrema of a function

programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation, allowing for machine learning based on gradient descent etc.

concept in calculus of variation

argument of the hyperbolic functions

theorem

generalization of the derivative

expression in calculus

In mathematics, in the area of combinatorics and quantum calculus, the '''q-derivative, or Jackson derivative', is a q''-analog of the ordinary derivative, introduced by Frank Hilton Jackson. It is the inverse of Jackson's q-integration. For other forms of q-derivative, see .

mathematical notion of infinitesimal difference

system of equations that either contains differential equations and algebraic equations

Method for solving linear differential equations using the Laplace transform

matrix whose columns are linearly independent solutions of a system of homogeneous linear ordinary differential equations

rate of change of the second derivative

publication by Leonhard Euler

calculus property