We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.


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 (x). We write '(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.

When using the limit definition, instead of using f(a), we just use f(x). Since x can be any value, the resulting limit will be a new brand new function. If we plug a point a into this function, the output will be f ' (a), the derivative of f at a.

People who Shmooped this also Shmooped...