Calculus Warm-UpFill in the blanks for #1-4.1. 2.

3. 4.

5. Find if and

6. Find if and

7. If, find and

8. If , find and

Calculus Warm-UpFill in the blanks for #1-4.1. 2.

3. 4.

5. Find if and

6. Find if and 7. If,

8. If

The Chain Rule

We already know and

The Chain Rule is just !!!

1. Find for Let , so

Both u and y are now easy to differentiate. and And so

The Chain Rule in words:The derivative of a composite function is the product of the derivatives of the outside and inside functions. The derivative of the outside function must be evaluated at the inside function.

If f and g are differentiable functions, then 2. Differentiate . Think of this as . Let

Chain Rule Practice Find .1.

2. Don’t use the quotient rule even though it would work!

3. You have to chain rule twice!!!

4.

a. Find where . b. Find where .

x

-2 7 -3 7 9

7 -2 -1 12 2

Chain Rule Practice Find .1.

2.

Chain Rule Practice Find .

3.

Chain Rule Practice 4.

a. Find where .

b. Find where .

x

-2 7 -3 7 9

7 -2 -1 12 2

Chain Rule Practice 4.

b. Find where .

x

-2 7 -3 7 9

7 -2 -1 12 2