Worksheet 12.2
Name___________________________________
Use the product rule to find the derivative.
1) f(x) = (4x - 3)(2x + 1)
1)
Objective: (12.2) Use Product Rule to Find Derivative
2) f(x) = (3x4 + 8)2
2)
Objective: (12.2) Use Product Rule to Find Derivative
3) (y-2 + y-1 )(4y-3 - 8y-4 )
3)
Objective: (12.2) Use Product Rule to Find Derivative
1
Use the quotient rule to find the derivative.
1
4) f(x) =
x7 + 2
4)
Objective: (12.2) Use Quotient Rule to Find Derivative
5) y =
x2 - 4
x
5)
Objective: (12.2) Use Quotient Rule to Find Derivative
6) y =
x2 + 8x + 3
x
6)
Objective: (12.2) Use Quotient Rule to Find Derivative
2
Write an equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated
value.
3x2 - 15
7) f(x) =
,x=0
7)
-3x - 3
Objective: (12.2) Find Equation of Tangent to Graph at Given Value
Solve the problem.
8) The total cost to produce x units of perfume is C(x) = (6x + 3)(4x + 2). Find the marginal
average cost function.
8)
Objective: (12.2) Solve Apps: Business and Science
9) A rectangular steel plate expands as it is heated. Find the rate of change of area with
respect to temperature T when the width is 1.3 cm and the length is 2.6 cm if
dl/dt = 1.7 x 10-5 cm/°C and dw/dt = 8.3 x 10-6 cm/°C.
Objective: (12.2) Solve Apps: Business and Science
3
9)
10) Assume that the temperature of a person during an illness is given by:
T(t) =
8t
+ 98.6,
2
t +1
where T = the temperature, in degrees Fahrenheit, at time t, in hours. Find the rate of
change of the temperature with respect to time.
Objective: (12.2) Solve Apps: Business and Science
4
10)
Answer Key
Testname: WORKSHEET12.2
1) f'(x) = 16x - 2
2) f'(x) = 72x7 + 192x 3
48 + 20y - 16y2
3)
y7
4) f'(x) = -
7x6
(x7 + 2)2
5)
dy
4
=1+
dx
x2
6)
dy 3x2 + 8x - 3
=
dx
2x3/2
7) y = - 5x + 5
6
8) 24 x2
9) 4.4 x 10-5 cm2 /°C
dT 8(1 - t2 )
=
10)
dt (t2 + 1)2
5