Module 1: The Calculus of Inverse Functions

In this module, you will learn about inverse functions. The module content is split into four lessons.

Project 1:
Use Logarithmic Differentiation to derive (show all the steps in order to establish) the following differentiation formulas:

The power rule: if $\frac{d}{dx}x^{r}=r\cdot x^{r-1}$
The product rule: If f and g are differentiable functions then ${(f\cdot g)}'=f\cdot {g}'+ {f}'\cdot g$
An extension of the product rule: If f, g, and h are differentiable functions then ${(f\cdot g\cdot h)}'= f\cdot g\cdot {h}'+ f\cdot{g}'\cdot h+{f}'\cdot g\cdot h$ .
The quotient rule: If f and g are differentiable functions with $g\neq 0,{(\frac{f}{g})}'=\frac{{f}'\cdot g-f\cdot {g}'}{g^{2}}$ .