Calculus Portal

Objective 1c: Derivatives of Inverse Functions

You will be able to find the derivative of an inverse function

Inverse Derivative Investigation

Let's look at two key problems from the Inverse Derivative Investigation. Questions 4 and 5 will help us inductively find a derivative rule for inverse functions. We will then use the Chain Rule to prove it. Duration: 11:55

Example 6

As Example 6 demonstrates, you can't always find an explicit equation for the inverse of a function. The derivative rule for inverse functions will come in handy in such a case. Duration: 7:13

Example 7

Example 7 presents another instance where finding an inverse of a function would be a fruitless endeavor. To find the derivative of its inverse we will once again find the reciprocal slope at the original function's y-value. Duration: 4:57

AP Multiple-Choice

The AP Exam will, of course, find clever ways for you to demonstrate your mastery of calculus, and Example 8 presents an instance of this. Here, you need to find the derivative of an inverse function for which you only have a collection of points. Pause this one and try it on your own. Duration: 3:23