# Related Rates 12/17 LizF

During class we did a group quiz re-take.  Then Mrs. Everard quickly introduced Related Rates.
Hw is finish the MC
Example number 1 from page 517
Find how fast z is changing when x=10

600=rate of change for x

# Class Notes: 12/7

Derivative of Inverse Functions:

Restrictions on the domain of the original function

Restrictions on the range of the inverse function

Graph:

Inverse of Inverse Tangent:

Inverse of Cosecant

Graph of Inverse Cosecant:

Inverse of Cotangent:

Graph of Inverse Cotangent:

Sample Problem:

Answers to 14-24 on Pg.151

Hw: Do 13-33 Odd on Pg.157

Inverse Trigonometric Functions

*see page 148 for graphs

\begin{align} \frac{d}{dx} \arcsin x & {}= \frac{1}{\sqrt{1-x^2}}\\ \frac{d}{dx} \arccos x & {}= \frac{-1}{\sqrt{1-x^2}}\\ \frac{d}{dx} \arctan x & {}= \frac{1}{1+x^2}\\ \frac{d}{dx} \arccot x & {}= \frac{-1}{1+x^2}\\ \frac{d}{dx} \arcsec x & {}= \frac{1}{x\,\sqrt{x^2-1}}\\ \frac{d}{dx} \arccsc x & {}= \frac{-1}{x\,\sqrt{x^2-1}} \end{align}

HW: Derive inverse csc, sec, cot

Also: pg.152 13-21 odd

# December 1 BJ

In class we went over the second Derivative Quiz and completed a worksheet on Implicit Differentiation.

Bonus problem on the quiz:

Implicit Differentiation problem: #12 on pg. 171

Homework:

– Read Section 4-5 on pgs. 145-148

– Review trig identities and the unit circle for a trigonometry quiz next class

# Natural Logs LizF

In class we found the derivative of natural logs and exponential functions

Derived that the derivative for the natural log is one over the argument

So…

To find the derivative of an exponential function take the natural logs of both sides. Don’t forget that y is a function of x so the chain rule applies.

# 11/18/2009 AS

In class we went over the homework. Here are the problems we went over and the equations we went over.

The homework is to finish test corrections for tuesday, and study for a quiz on identities and the unit circle.