# Instantaneous Rate of Change Calculator

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

## What is the Instantaneous Rate of Change Calculator?

'**Instantaneous Rate of Change Calculator**' is an online tool that helps to calculate the rate of change for a given function. Online Instantaneous Rate of Change Calculator helps you to calculate the rate of change within a few seconds.

### Instantaneous Rate of Change Calculator

## How to Use Instantaneous Rate of Change Calculator?

Please follow the steps below on how to use the calculator:

**Step1:**Enter the function with respect to x and the value of x in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the rate of change for a given function**Step 3:**Click on the**"Reset"**button to clear the fields and enter new values.

## How to Find Instantaneous Rate of Change Calculator?

Instantaneous rate of change is defined at the rate of change at a particular point or it is the rate of change in derivative of the function at a particular point.

Let y = f(x) be the function at a point x = a, rate of change = dy / dx at x = a

Let's see an example to understand briefly.

**Solved Examples on Instantaneous Rate of Change Calculator**

**Example 1:**

Find the instantaneous rate of change for the function y = 3x^{2} at x = 2

**Solution:**

Given: Function y = 3x^{2}

The instantaneous rate of change is dy / dx = 6x

When x = 2,

Instataneous rate of change = 6(2)

= 12

Therefore, the instantaneous rate of change is 12

**Example 2:**

Find the instantaneous rate of change for the function y = -2x^{2} at x = -4

**Solution:**

Given: Function y = -2x^{2}

The instantaneous rate of change is dy / dx = -4x

When x = -4,

Instataneous rate of change = -4(-4)

= 16

Therefore, the instantaneous rate of change is 16

**Example 3:**

Find the instantaneous rate of change for the function y = 5x^{3} at x = 3

**Solution:**

Given: Function y = 5x^{3}

The instantaneous rate of change is dy / dx = 15x^{2}

When x = 3,

Instataneous rate of change = 15(9)

= 135

Therefore, the instantaneous rate of change is 135

Similarly, you can try the calculator to find the instantaneous rate of change for

- y = f(x) = 2x
^{3}+ 4x at x = 5 - y = f(x) = 7x + 5 at x = 3

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