The Derivative Function
The "derivative of f at a," written f ' (a), is a number that is equal to the slope of the function f at a.
For any differentiable function f there is another function, known as the derivative of f and written f ' (x). We write f '(x) to show that this is a function.
We can calculate the derivative function using the limit definition in the same way we calculated the value of the derivative at a point using the limit definition.