3.2 – The Product and Quotient Rule Math& 151 Warnock - Class Notes

We have seen that _________c f x

and ______________f x g x

.

Let’s investigate f x g x

. Do you think it is __________________?

Examine with f x x and 2g x x .

Let’s use the definition of the derivative to discover it.

Let y f x g x , hint: f x h g x

0

limh

dydx

#1) Given xf x xe , find f x and n

f x .

#2) Differentiate the function f t t a bt .

#3) If f x x g x , where 9 ___g and 9 ___g , find 9f .

Let’s use the definition of the derivative to discover the quotient rule.

Let

f xy

g x hint: f x g x

0

limh

dydx

#4) Let 2

3

2 3

2 3

x xy

x

, find y.

#5) Find an equation of the tangent line to the curve 21

xey

x

at the point 1,

2e

.

Table of Differentiation Formulas