Fall ‘09
MATH 176
Group Assignment #18
DERIVATIVES: THE PRODUCT & QUOTIENT RULES
The Product Rule
For the following questions, consider the functions
1) What is
2) Compute
and
.
?
.
3) In a previous activity, we learned that the derivative of a sum of functions is the sum of
the derivatives, i.e.,
. Is the same true for the
derivative of a product of functions, i.e., that
check, compute
4) How does
,
, and
compare to
? To
.
?
Fall ‘09
MATH 176
The Product Rule
If
and
are differentiable functions, then
.
The product rule can also be written
In words: The derivative of a product is the derivative of the first times the second, plus the first
times the derivative of the second.
The Quotient Rule
For the following questions, consider the functions
1) What is
2) Compute
and
.
?
.
3) Is it true that the derivative of a quotient of functions is the quotient of their derivative,
i.e., that
4) How does
? To check, compute
compare to
?
,
, and
.
Fall ‘09
MATH 176
The Quotient Rule
If
and
are differentiable functions, then
,
or equivalently,
.
In words: The derivative of a quotient is the derivative of the numerator time the denominator
minus the numerator times the derivative of the denominator, all over the denominator squared.
Practice Problems
Using the ideas from the previous page and the product rule or quotient rule compute the
derivatives for the following functions:
1)
2)
3)
MATH 176
4)
5)
6)
7)
Suggested Homework Problems
Chapter 3 Review: p. 166: #7, 13,17,21,29,31,34,41
p. 167: #56, 58, 61, 64, 66
Section 4.1: #1-4, 14, 15,16,18, 21, 22, 26, 28
Fall ‘09