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) = x3

  • Its derivative is f'(x) = 3x2
  • The derivative of 3x2 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.