# Partial Derivative Calculator

## Introduction to Partial Derivative Calculator

Partial Derivative Calculator step by step is an online tool that is helpful to find the partial derivative of a function. The calculator of partial derivatives uses the differential rule to find the partial derivative of a given function.

Since the partial derivative is a part of the calculus, it also has similarities with the derivative. So this concept is somehow confusing for students. So here we introduce online software capable of differentiating these two concepts.

## What is a Partial Differentiation Calculator?

A partial calculator is an online tool that differentiates a function of several variables for one variable and treats other variables as constants. Partial derivative calculator with steps follows all the derivative rules like chain rule, product rule and quotient rule to perform partial differentiation on a function.

While computing partial derivatives by hand, sometimes you may be confused or forget a variable to differentiate. Multivariable partial derivative calculator helps handle such cases simply and easily.

## How to Calculate a Partial Derivative

There are some simple steps to using Partial Derivatives Calculator; these are:

1. Write the function in the "Enter Function" box. Or, if you don't know how to use it, you can try the "Load Example" option.
2. In the second step, you need to choose the variable from the drop-down list of the "With Respect to" box.
3. Now choose the number from the "Time" box; it is how many times you want to calculate a function's partial derivative.
4. In the last step, click on the "Calculate" button.

After clicking the Calculate button, the website will start execution and perform derivation on the given function. You will get your result within a few seconds!!

## Formula used by Partial Calculator

Since the derivative of a function computes the rate of change for a variable. But in the case of partial differentiation, the function may contain more than one or two variables for which the rate of change is being calculated.

Free Partial Derivative Calculator follows the derivative rule, chain rule, product rule, and power rule. It calculates the function's derivative for one variable by treating other variables as constants.

Working of the partial derivative of a multivariable function calculator can be understood by the example below.

Example:

Let (?, ?) = ? + ? where ? = ? 2 and = ? 2 . Partial Derivative will be computed using the following formula:

$$\frac{df}{dx} \;=\; \frac{df}{du} \frac{du}{dx} \;+\; \frac{df}{dv} \frac{dv}{dx}$$

And

$$\frac{df}{dy} \;=\; \frac{df}{du} \frac{du}{dy} \;+\; \frac{df}{dv} \frac{dv}{dy}$$

Now differentiate u with respect to x and with respect to y.

$$\frac{du}{dx} \;=\; 2x$$ $$\frac{du}{dy} \;=\; 0$$

And differentiating v with respect to x and y.

$$\frac{dv}{dx} \;=\; 0$$

(Since v contains only y variable so it will be treated as constant to differentiate with respect to x and vice versa)

$$\frac{dv}{dy} \;=\; 2y$$

Differentiate f(x,y) with respect to u and v.

$$\frac{df}{du} \;=\; 1$$ $$\frac{df}{dv} \;=\; 1$$

So,

$$f_x \;=\; \frac{df}{dx} \;=\; 2x$$

And

$$f_y \;=\; \frac{df}{dy} \;=\; 2y$$

fx and fy represents the partial derivative of f with respect to x and y respectively. Partial derivatives are useful in analyzing surfaces for maximum and minimum points.

## Why use a Multivariable Calculator Partial Derivative?

Like derivative, partial derivative is also an essential part of calculus because both are fundamental solutions to different problems in calculus. Partial Derivative Calculator with steps helps you to find these complete solutions step by step.

This calculator not only computes the partial derivative of a given function. It also represents the function graphically with respect to its change so that users may understand the solution easily.

In mathematics, there are a lot of concepts for which students always search for help online. Partial calculators help them to clear concepts. Because it helps the students focus on the idea, you need to use this derivative calculator.

## Benefits of using partial derivative of multivariable function calculator

A Partial Derivative Calculator is an efficient tool with many benefits. These are:

1. It is an efficient tool because it executes fast and shows results within a few moments.
2. This calculator is easy to use because it contains simple steps. You need to write the function on its website.
3. Partial calculator is a free online tool made for only educational purposes.
4. Partial derivatives calculator plots a 3D graph according to the rate of change of a given function.
5. Calculator partial derivative simplifies the solution quickly and provides all possible steps.
6. You can also select the number up to which you want to find the partial derivative.
7. This calculator does not charge any cost because it is free of cost.
8. This tool calculates partial derivatives of function and explains every step so that the user can easily understand it.
9. Partial derivative calculator step by step verifies the results by integrating it.
10. This partial derivative solver computes the derivative of a given function with respect to one variable and treats other variables as constants.
11. You can focus on understanding the concept instead of wasting time on manual calculations.

### Shaun Murphy

Last Updated March 28, 2022

A professional content writer who likes to write on science, technology and education.