Partial derivative online calculator

Partial derivative concept is only valid for multivariable functions. Examine two variable function z=f(x,y). Partial derivative by variables and 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 by the variables and correspondingly. Derivatives 2zxy and 2zyx are called mixed derivatives of the function by the variables , and , correspondingly. If the function 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 two times by the variable and three times by the variable 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
Tangent equation online calculator
Normal equation online calculator

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