Second Derivative

How to find the second derivative of a function: definition, 1 example, and its solution.

Definition

Definition

The second derivative is the derivative of a derivative.
So, to find the second derivative,
differentiate the function [twice].

It is written as f''(x), y'', d2y/dx2, (d2/dx)f(x).

Example

Example

Solution

First find the derivative f'(x).

f(x) = x5 - 7x2 - 8x + 1.
Then f'(x) = 5x4 - 7⋅2x1 - 8 + 0.

Derivative of a Polynomial

-7⋅2x1 = -14x

f'(x) = 5x4 - 14x - 8.

To find f''(x), differentiate again:
find the derivative of f'(x).

Then f''(x) = 5⋅4x3 - 14 - 0.

5⋅4x3 = 20x3

So f''(x) = 20x3 - 14.