# Partial Derivative Calculator

Partial derivatives are defined as finding the rate of change of a function with respect to one variable. It deals with the variables such as x and y, functions f(x), and the corresponding changes in the variables x and y.

## What is a Partial Derivative Calculator?

'Cuemath's Partial Derivative Calculator' is an online tool that helps to calculate the value of the partial derivatives. Cuemath's online Partial Derivative Calculator helps you to calculate the value of the partial derivatives in a few seconds.

## How to Use Partial Derivative Calculator?

Please follow the below steps to find the value of the partial derivatives:

**Step 1:**Enter the function with respect to x and y in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the value of the partial derivatives.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How to Find Partial Derivative Calculator?

The partial derivative of a function is represented by ∂. Let f(x,y) be a function with variable x and y

∂f / ∂x means that the function is the derivative of f with respect to the variable x.

∂f / ∂y means that the function is the derivative of f with respect to the variable y.

There are common functions and rules we follow to find derivatives

**Solved Example:**

Find the partial derivative value of 5x^{3} + 2y^{2}

**Solution:**

Given: f(x,y) =** **5x^{3} + 2y^{2}

∂f / ∂x = ∂ / ∂x(** **5x^{3} + 2y^{2})

Using multiplication by constant and power rule,

= ∂ / ∂x(5x^{3} + 2y^{2})

= ∂ / ∂x(5x^{3}) + ∂ / ∂x(2y^{2})

= 5 × 3x^{3 - 1} + 0

= 15x^{2}

∂f / ∂y = ∂ / ∂y(** **5x^{3} + 2y^{2})

Using multiplication by constant and power rule,

= ∂ / ∂y(5x^{3}) + ∂ / ∂y(2y^{2})

= 0 + 2 × 2y^{2 - 1}

= 4y

Therefore, the partial derivative value of 5x^{3} + 2x^{2 }with respect to x and y is 15x^{2} and 4x.

Similarly, you can use the calculator to find the value of partial derivatives for the following:

- x
^{3}/ 2y - 5x
^{2}+ 6y^{4}