Lesson Plan #6

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Lesson Plan #17

Class: AP Calculus Date: Monday October 18th, 2010

Topic: The Chain Rule

Aim: How do we use the chain rule to find the derivative of a function?

Objectives:

1) Students will be able to use the chain rule to find the derivative of a function.

HW# 17: Show ALL work!

Find an equation of the line tangent to the graph of [pic]at the point [pic]where[pic].

Do Now:

1) At which point(s) does the graph of [pic] has a horizontal tangent line.

Write the Aim and Do Now

Get students working!

Take attendance

Give back work

Go over the HW

Collect HW

Go over the Do Now

Suppose we had to find the derivative of [pic]. We have a rule to differentiate x to some power, such as [pic], but not an expression to some power, such as [pic]

Let’s examine the function [pic]

First find [pic], which means the derivative of y with respect to x?

Now let [pic]= [pic]

So we have [pic]

Next find [pic]

Next find [pic]

Notice that [pic]

This known as the chain rule to find the derivative of a composite function.

You can think of the chain rule like this

If [pic], where [pic]is some expression, then [pic]

Another way to think of it is that it is like the power rule, except that you have to then multiply by the derivative of the inside.

For each of the following, find [pic].

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

7) [pic]

8) [pic]

Sample Test Questions:

1) If[pic], then find[pic].

2) If[pic], then find [pic]

3) If [pic], then find [pic]

4) If[pic], find [pic]

A) [pic] B) [pic] C) [pic] D) [pic] E) [pic]

5) If [pic], find [pic]

A) [pic] B) [pic] C) [pic] D) [pic]

E) [pic]

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