Ads
related to: how to find the derivative with respect to x calculator formula
Search results
Results From The WOW.Com Content Network
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.
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
In calculus, the differential represents the principal part of the change in a function = with respect to changes in the independent variable. The differential is defined by = ′ (), where ′ is the derivative of f with respect to , and is an additional real variable (so that is a function of and ).
The complex-step derivative formula is only valid for calculating first-order derivatives. A generalization of the above for calculating derivatives of any order employs multicomplex numbers, resulting in multicomplex derivatives.
In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A. [ 1 ] If A is a differentiable map from the real numbers to n × n matrices, then
The derivatives in the table above are for when the range of the inverse secant is [,] and when the range of the inverse cosecant is [,]. It is common to additionally define an inverse tangent function with two arguments , arctan ( y , x ) {\textstyle \arctan(y,x)} .
The rate of change of f with respect to x is usually the partial derivative of f with respect to x; in this case, =. However, if y depends on x, the partial derivative does not give the true rate of change of f as x changes because the partial derivative assumes that y is fixed. Suppose we are constrained to the line
If y is a function of x, then the differential dy of y is related to dx by the formula =, where denotes not 'dy divided by dx' as one would intuitively read, but 'the derivative of y with respect to x '. This formula summarizes the idea that the derivative of y with respect to x is the limit of the ratio of differences Δy/Δx as Δx approaches ...