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 = 3x² at x = 2

Solution:

Given: Function y = 3x²

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 = -2x² at x = -4

Solution:

Given: Function y = -2x²

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 = 5x³ at x = 3

Solution:

Given: Function y = 5x³

The instantaneous rate of change is dy / dx = 15x²

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) = 2x³ + 4x at x = 5
• y = f(x) = 7x + 5 at x = 3

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