# Second Derivative

(Read about derivatives first if you don't already know what they are!)

A derivative basically gives you the slope of a function at any point.

The "Second Derivative" is **the derivative of** the derivative of a function. So:

- Find the derivative of a function
- Then take the derivative of that

A derivative is often shown with a little tick mark f'(x)

The second derivative is shown with **two** tick marks like this: f''(x)

### Example: f(x) = x^{3}

- Its derivative is
**f'(x) = 3x**^{2} - The derivative of 3x
^{2}is 6x, so the second derivative of f(x) is:

f''(x) = 6x

Here you can see the derivative f'(x) and the second derivative f''(x) of some common functions:

Notice how the slope of each of those functions is the derivative plotted below it.