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# Partial Derivative Calculator

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Let us assume a function f with two variables, i.e., f(x, y). Keeping y as constant and differentiating f with respect to x, we get the partial derivative of f function with respect to x, denoted as $\frac{\partial f}{\partial x}$ or $f_x$.

Similarly, keeping x as constant and differentiating f with respect to y, we get the partial derivative of f function with respect to y, denoted as $\frac{\partial f}{\partial y}$ or $f_y$.

Plug in the function with two variables into the partial derivative calculator to get the partial derivative of the given function.

## Steps

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Step 1 : Note down the given f function with their two variables x and y.

Step 2 : Find the partial derivative according to the problem, if it is with respect to x, then find $\frac{\partial f}{\partial x}$ or if it is with respect to y, then find $\frac{\partial f}{\partial y}$.

## Problems

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Based on partial derivative, some of the problems are given below.

### Solved Examples

Question 1: If $f(x,y)$ = $x^{2}y + 2x$, find the partial derivative $f_x$.
Solution:

Step 1 : Given : $f(x,y)$ = $x^{2}y+2x$.

Step 2 : $\frac{\partial f}{\partial x}$ = $\frac{\partial }{\partial x}$$(x^{2}y+2x) = \frac{\partial }{\partial x}$$(x^{2}y)$ + $\frac{\partial }{\partial x}$$(2x) = (2xy) + (2) = 2xy + 2 Therefore, partial derivative of x^{2}y+2x = 2xy + 2. Question 2: if f(x,y) = xe^{xy}, find the partial derivative f_y Solution: Step 1 : Given : f(x,y) = xe^{xy} Step 2 : \frac{\partial f}{\partial y} = \frac{\partial }{\partial y}$$(xe^{xy})$

= $(x)(xe^{xy})$ = $x^{2}e^{xy}$

Therefore, partial derivative of $xe^{xy}$ = $x^{2}e^{xy}$.