AP CALCULUS

1009 : Product and Quotient Rules

PRODUCT RULE FOR DERIVATIVES

 Product Rule:

 

(In Words) ________________________________________________

( ) ( )y f x g x

2( ) (3 2 )(5 4 )f x x x x

y u v

PRODUCT RULE FOR DERIVATIVES

2( ) (3 2 )(5 4 )f x x x x EX:

Example Using the Product Rule

3 2Find if 4 3f x f x x x

3 2

3 2 3 2 2

4 4 2

4 2

Using the Product Rule with 4 and 3,gives

4 3 4 2 3 3

2 8 3 9

5 9 8

u x v x

df x x x x x x x

dx

x x x x

x x x

GRADING:

PRODUCT RULE FOR DERIVATIVES

duv

dx

EX: Given u and v are differentiable at x = 2 and

u(2) = 3 u’(2) = 4 v(2) = - 2 v’(2) = 5

QUOTIENT RULES FOR DERIVATIVES

If you can reduce the fraction - - - - - DO

1( )

xf x

x

2 4 3( )

x xf x

x

QUOTIENT RULES FOR DERIVATIVES

Quotient Rule:

 

(In Words) _______________________________________________

¡ ¡ ¡ ¡ WATCH YOUR ALGEBRA ! ! ! !

22 4 3( )

2 3

x xf x

x

( )

( )

f xy

g x

uy

v

QUOTIENT RULES FOR DERIVATIVES

22 4 3( )

2 3

x xf x

x

EX:

Example Using the Quotient Rule

3

2

4Find if

3

xf x f x

x

3 2

3 2 2 3

22 2

4 2 4

22

4 2

22

Using the Quotient Rule with 4 and 3,gives

4 3 3 4 2

3 3

3 9 2 8

3

9 8

3

u x v x

x x x x xdf x

dx x x

x x x x

x

x x x

x

GRADING:

QUOTIENT RULES FOR DERIVATIVES

2

1( )

4 3f x

x x

EX:

QUOTIENT RULE FOR DERIVATIVES

d u

dx v

EX: Given u and v are differentiable at x = 2 and

u(2) = 3 u’(2) = 4 v(2) = - 2 v’(2) = 5

Last Update

• 9/17/10

Assignment: p 124 # 15 - 35 odd omit 19