Partial derivative online calculator

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Partial derivative concept is only valid for multivariable functions. Examine two variable function z=f(x,y). Partial derivative by variables x and y are denoted as partial derivative of function z by variable x and partial derivative of function z by variable y correspondingly. The partial derivatives partial derivative of function z by variable x and partial derivative of function z by variable y by themselfs are also the two variable functions: partial derivative of function z by variable x and partial derivative of function z by variable y , so their partial derivatives can also be found:

partial derivative of function p by variable x

partial derivative of function q by variable y

partial derivative of function p by variable y

partial derivative of function q by variable x

Derivatives second order partial derivative of function z by variable x and second order partial derivative of function z by variable y are the second order partial derivatives of the function z by the variables x and y correspondingly. Derivatives mixed derivative of the function z by the variables x and y and mixed derivative of the function z by the variables y and x are called mixed derivatives of the function z by the variables x, y and y, x correspondingly. If the function z and their mixed derivatives mixed derivative of the function z by the variables x and y and mixed derivative of the function z by the variables y and x are defined at some neighborhood of a point M(x0,y0) and continuous at that point, then the following equality is valid:

equality of mixed derivatives

Similary, one can introduce the higher order derivatives, for instance частная производная высокого порядка means that we should differentiate the function z two times by the variable x and three times by the variable y so:

partial derivative decomposition

Sometimes, in order to denote partial derivatives of some function z=f(x,y) notations: fx'(x,y) and fy'(x,y), are used. Subscript index is used to indicate the differentiation variable. Using this approach one can denote mixed derivatives: fxy''(x,y) and fyx''(x,y) and also the second and higher order derivatives: fxx''(x,y) and fxxy'''(x,y) accordingly. Following notations are equivalent:

equivalent notations of the partial derivative

To denote partial derivatives in our online calculator, we use symbols: partial derivative of function z by variable x ; partial derivative of function z by variable y ; partial derivative of function z . Sample of step by step solution can be found here.

Partial derivative calculator
Function to calculate partial derivative
Input the expression which partial derivative you want to calculate:


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Other useful links:

Online derivative calculator
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Normal equation online calculator

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