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# Second Derivative Calculator

Derivatives are defined as finding the rate of change of a function with respect to other variables.

## What is Second Derivative Calculator?

'**Second Derivative Calculator**' is an online tool that helps to calculate the value of the second derivative for a given function. Online Second Derivative Calculator helps you to calculate the value of the second derivative in a few seconds.

### Second Derivative Calculator

## How to Use Second Derivative Calculator?

Please follow the below steps to find the value of the second derivative:

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

## How to Find Second Derivative Calculator?

Derivatives deals with the variables such as x and y, functions f(x), and the corresponding changes in the variables x and y. The derivative of a function is represented by f '(x). It means that the function is the derivative of y with respect to the variable x. The symbol dy and dx are called differentials. The process of finding derivatives is called differentiation.

The **second derivative** is defined as the derivative of the derivative of a function also known as double differentiation of given function. It is represented by f ''(x) or d^{2}f / dx^{2}

There are common functions and rules we follow to find derivatives

**Solved Examples on Second Derivative Calculator**

**Example 1:**

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

**Solution:**

f '(x) = d / dx( 5x^{3} + 2x^{2})

= d / dx ( 5x^{3}) + d / dx(2x^{2})

Using multiplication by constant and power rule,

= (5 × 3x^{3 - 1}) + (2 × 2x^{2 - 1})

= 15x^{2} + 4x

f ''(x) = d^{2}f / dx^{2}

= d / dx(15x^{2} + 4x)

= 30x + 4

Therefore, the second derivative value of 5x^{3} + 2x^{2 }is 30x + 4

**Example 2:**

Find the second derivative value of 8x^{4} - x^{2} + 4x + 5

**Solution:**

f '(x) = d / dx( 8x^{4} - x^{2} + 4x + 5)

= d / dx ( 8x^{4}) - d / dx(x^{2}) + d / dx(4x) + d / dx(5)

Using multiplication by constant and power rule,

= (8 × 4x^{4 - 1}) - (2x^{2 - 1}) + 4 + 0

= 32x^{3} - 2x + 4

f ''(x) = d^{2}f / dx^{2}

= d / dx(32x^{3} - 2x + 4)

= 32(3x^{3 - 1}) - 2

= 96x^{2} - 2

Therefore, the second derivative value of 8x^{4} - x^{2} + 4x + 5^{ }is 96x^{2} - 2

Similarly, you can use the calculator to find the value of the second derivative for the following:

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

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