December 6, 2012AIM: How do we find the derivative

of quotients?

Do Now: Find the derivatives

HW2.3b Pg. 126 - 128 #7 – 11 odd, 15, 65, 81, 95, 105 – 108

xexf x cos)()1

x

xxg

sin)()2

How can we find the derivative of

2

4)(

2

x

xxh

The Quotient RuleHow can we find the derivative of

Or, we can use the Quotient Rule:If f and g are differentiable functions, then f/g

is a differentiable for all x such that g(x) ≠ 0, and

“The bottom times the derivative of the top minus the top times the derivative of the bottom over the bottom squared”

2

4)(

2

x

xxh

2

'

)(

)(')()(')()(

xg

xgxfxfxgx

g

f

Example

Use the product rule to find the derivative of

Step 1: Define f(x) and g(x)Step 2: Find f’(x) and g’(x)Step 3: Plug into formula and simplify

2

4)(

2

x

xxh

Practice

1. Find

2. Find

1

42 xx

x

dx

d

1)(,

21 x

xxh

dx

dhx

1.

2.

3.

6.

4.

5.

Practice!