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Partial Derivative Calculator
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If f(x,y) is a function, then the differentiation of f with respect to x keeping y as constant is called as partial derivative of f with respect to x which is denoted by $\frac{\partial f}{\partial x}$ or $f_{x}$. Similarly the differentiation of f with respect to y keeping x as constant is called as partial derivative of f with respect to y which is denoted by $\frac{\partial f}{\partial y}$ or $f_{y}$. Online Partial Derivative Calculator (known as partial differentiation calculator) is a tool which makes calculations easy and fun. It is used to calculate the partial differentiation of a function with two variables. It even intake multivariables hence also known as multivariable derivative calculator or partial differential equation solver online that is a funfull tool in math. You have to enter the function and variable value to get answer instantly.
Below is given a default function with two variables. Click on "Submit", it will calculate partial derivative of function with respect to x keeping y as constant and vice verse.

Steps for Partial Derivative

Step 1 :

Observe the given function with two variables.

Step 2 :

$\Rightarrow$ To find the partial derivative of f with respect to x which is denoted by $\frac{\partial f}{\partial x}$ or f$_{x}$, differentiate f with respect to x keeping y as constant.

$\Rightarrow$ To find the partial derivative of f with respect to y which is denoted by $\frac{\partial f}{\partial y}$ or f$_{y}$, differentiate f with respect to y keeping x as constant.

Examples on Partial Derivative Calculator

1. If f(x, y) = xy + x3 then calculate $\frac{\partial f}{\partial x}$ ?

Step 1 :

Given function: f(x, y) = xy + x3

Step 2 :

$\frac{\partial f}{\partial x}$ = $\frac{\mathrm{d} }{\mathrm{d} x}$ (x3) + y $\frac{\mathrm{d} (x)}4{\mathrm{d} x}$

=> 3x2 + y

3x2 + y

2. If f(x, y) = y2 x3 then calculate $\frac{\partial f}{\partial y}$ ?

Step 1 :

Given function: f(x, y)  = y2 x3

Step 2 :

$\frac{\partial f}{\partial y}$ = x3 $\frac{\mathrm{d} (y)^{2}}{\mathrm{d} y}$

=> x3 2y