# Derivatives of Exponential, Logarithmic and Inverse Functions

## 3.1 Derivative of the Inverse of a Function

There is the relationship between the dierivative of a function and the derivative of its inverse.  You will explore this as part of today's lesson.

You will also begin looking at inverse of trigonometric functions.  In order to make the inverse a function, we need to restrict the domain of the trigonometric function.

Resources

• Notes

Assignment

• p162 #20
• p162 #1-5, 7, 10

## 3.5 Derivatives of Exponential Functions

Derivatives of exponential functions are based on the exponential function.  The derivative is pretty basic, and you should be able to follow the proof, but will not need to know it for your test.

Assignment: p170 #1-17, 41, 47, 49

## 3.6 Derivatives of Logarithmic Functions

Today, we will find the derivative of y = ln x using the fact that it is the inverse of the function y = e^x.  There are a couple of different ways to determine this, and we will make use of the properties of logarithms to differentiate more complicated logarithmic functions as well.

Assignment p170 #19-39

## 3.7 Logarithmic Differentiation

Some functions could be very complicated when we try to differentiate them, as they may be a mix of several product rule, quotient rule and chain rule problems strung together.  One way to simplify the problem is using the properties of logarithms.

Recall that for y = ln (ab) can be rewritten as y= lna + lnb and that y=ln(a/b) can be rewritten as y= lna - lnb

Assignment p170 #43-46, 48, 52, 53