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 d²f / dx²

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 5x³ + 2x²

Solution:

f '(x) = d / dx( 5x³ + 2x²)

= d / dx ( 5x³) + d / dx(2x²)

Using multiplication by constant and power rule,

= (5 × 3x^{3 - 1}) + (2 × 2x^{2 - 1})

= 15x² + 4x

f ''(x) = d²f / dx²

= d / dx(15x² + 4x)

= 30x + 4

Therefore, the second derivative value of 5x³ + 2x² is 30x + 4

Example 2:

Find the second derivative value of 8x⁴ - x² + 4x + 5

Solution:

f '(x) = d / dx( 8x⁴ - x² + 4x + 5)

= d / dx ( 8x⁴) - d / dx(x²) + d / dx(4x) + d / dx(5)

Using multiplication by constant and power rule,

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

= 32x³ - 2x + 4

f ''(x) = d²f / dx²

= d / dx(32x³ - 2x + 4)

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

= 96x² - 2

Therefore, the second derivative value of 8x⁴ - x² + 4x + 5 is 96x² - 2

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

• x³ / 2
• 5x² + 6y²

☛ Related Articles:

• Derivative Formula
• Integration

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