(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.