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 zx and zy correspondingly. The partial derivatives zx and zy by themselfs are also the two variable functions: zxpx,y and zyqx,y , so their partial derivatives can also be found:

pxxzx2zx2

qyyzy2zy2

pyyzx2zxy

qxxzy2zyx

Derivatives 2zx2 and 2zy2 are the second order partial derivatives of the function z by the variables x and y correspondingly. Derivatives 2zxy and 2zyx 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 2zxy and 2zyx are defined at some neighborhood of a point M(x0,y0) and continuous at that point, then the following equality is valid:

2zxy2zyx

Similary, one can introduce the higher order derivatives, for instance 5zx2y3 means that we should differentiate the function z two times by the variable x and three times by the variable y so:

5zx2y33y32zx2yyyxzx

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: zx ; zy ; 5zx2y3 . Sample of step by step solution can be found here.

Partial derivative calculator
2xyxycosxy
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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