Lesson Plan: Differentiation of Inverse Functions Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the derivatives of inverse functions.
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.
Students should already be familiar with
- the chain, product, and quotient rules for differentiation,
- differentiating polynomial, trigonometric, rational, and exponential functions.
Students will not cover
- derivatives of logarithmic functions in detail,
- derivatives of inverse trigonometric functions.