4.2 - DERIVATIVES - PRODUCTS AND QUOTIENTS
I.
Product Rule
y  f (x )
= g ( x )  h( x )
y  = f ( x) = g ( x)  h( x) + h( x )  g ( x)
OR
y  = f ( x) = g ( x)  h( x ) + h( x)  g ( x)
(since multiplication is commutative)
Examples:
II.
Quotient Rule
y = f ( x) =
t ( x)
b( x )
y  = f ( x) =
b( x)  t ( x)  t ( x)  b( x)
 b( x ) 2
(don’t forget that subtraction is not
commutative, so you cannot switch
the order in the numerator)
Examples:
III. Marginal Average Cost, Revenue, and Profit
Definitions:
Cost Analysis: A machine shop makes drill bits with
C ( x )  1000  25 x  0.1x 2 .
a. Find the average cost function for drill bits.
b. Find the average cost of producing a drill bit at a production level of 10 drill bits per day and
interpret.
c. Estimate the average cost per bit at a production level of 11 drill bits per day and interpret.