Second Derivative Calculator

Second Derivative Calculator

This calculator finds the second derivative of a function. The entered equation is displayed in the arranged form. This calculator also finds the first derivative.

By clicking on the “+” symbol in the results you can see all the steps involved to calculate the second derivative.

What is the second derivative?

The second derivative refers to the differentiation performed for the second time on the same function. 

It is similar to the first differentiation. The only possible difference is the notation. The second differentiation is represented by f’’(x) or d2y/dx2.

How to find the second derivative?

We simply use the rules of derivatives to find the second derivative. The process is the same as the first derivative. 

Example:

Find the second derivative for 5x³.

Solution:

Step 1: Perform the first-order differentiation.

f’(x) = 5x³

f’(x) = 5.3 x^3-1 (using the power rule)

f’(x) = 15 x²

Step 2: Find the second-order differentiation.

f’’(x) = 15 x²

f’’(x) = 15.2 x^2-1 (using the power rule)

f’’(x) = 30 x