# What is a second derivative?

Mar 10, 2018

See below.

#### Explanation:

The second derivative is the derivative of the derivative of a function.

Let's take a random function, say $f \left(x\right) = {x}^{3}$. The derivative of $f \left(x\right)$, that is, $f ' \left(x\right)$, is equal to $3 {x}^{2}$.

The second derivative of ${x}^{3}$ is the derivative of $3 {x}^{2}$. That's $6 x$.

So we say that the second derivative of $f \left(x\right) = {x}^{3}$, or $f ' ' \left(x\right)$, is equal to $6 x$