Lesson: Differentiation of Inverse Functions Mathematics • Higher Education

In this lesson, we will learn how to find the derivatives of inverse functions.

Lesson Plan

Students will be able to

understand that for a continuously differentiable function with nonzero derivative at a point , the derivative of the inverse function at is given by ,
use this equation to find derivatives of familiar inverse functions, such as the natural logarithm,
understand the statement of the inverse function theorem,
use the inverse function theorem to find derivatives of inverse functions when we do not have an explicit formula for the inverse function.

Lesson Video

Lesson Explainer

Lesson Worksheet

Q1:

For the function at , find .

Q2:

A wall is 15 feet high. An angle is formed when a ladder of length is placed against the wall such that the top of the ladder is at the top of the wall, as shown in the figure. The ladder's length can be changed, but the top of the ladder always remains at the top of the wall. Find the rate of change, to the nearest ten thousandth, of the angle when the ladder has a length of 21 feet.

Q3:

If , , and , find .