Second Derivative

Second Derivative

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

Definition

The second derivative can be found by differentiating a function twice. So it is written as f''(x), y'', (d^2y/dx^2), d^2/dx*f(x).

The second derivative can be found
by differentiating a function twice.

So it is written as
f''(x), y'', d2y/dx2, (d2/dx2)f(x), ... .

Example

For the given f(x), find f''(x). f(x) = x^5 - 7x^2 + 1

First, differentiate f(x).

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

Derivatives of polynomials

Then, differentiate f'(x) again.

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