3.3

Term

1 / 10

1.
If f(x) =2 (4x^(2)−2)^(3)
then f′(x) =
and f′(1) =
2.
If f(x) =ln(6x^(2)+2)
then f′(x) =
and f′(6) =

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Terms in this set (10)

1.
If f(x) =2 (4x^(2)−2)^(3)
then f′(x) =
and f′(1) =
2.
If f(x) =ln(6x^(2)+2)
then f′(x) =
and f′(6) =

a) 2(3(4x^(2)-2)^(2)*(8x))
=48x(4x^(2)-2)^(2)
b)48(4-2)^(2)
=48*4
=192
c) (1/(6x^(2)+2))*(12x)
=(12x/6x^(2)+2)
=(6x/3x^(2)+1)
d)(6(6)/3(6^(2))+1)
=36/109

2.
The price in dollars of a house during a period of mild inflation is described by the formula P(t) =92000e^(0.03t), where t is the number of years after 1990. Answer the following questions:
A. The value of the house in the year 2000 will be _____ dollars. (Round your answer to the nearest dollar.)
B. In the year 2000 the value will be increasing at a rate of _____ dollars per year. (Round your answer to the nearest dollar.)
C. How long will it take for a house to double in value? Answer: ____ years. (Round your answer to two decimal places.)

a)92000e^(.03)
b)2760e^(.3)=P'(10)
P'(t)=9200(e^(.03t)*(.03))
=2760e^(.03t)
c)92000(e^.03)^t
doubling time= (ln(2)/lne(^.03))
=(ln2/(.03)lne^(1))
=ln2/.03

3.
Find the derivative of w= (t^(4)−4)^64

64(t^(4)-4)^(63)*(4t^(3))
=256t^(3)(t^(4)-4)^63

4.
Find the derivative of w= (14−6r)^8

8(14-6r)^(7)*(-6)
=-48(14-6r)^7

5.
Find the derivative of y= ^(5)√s^(7)+12

=(s^(7)+12)^(1/5)
y'=1/5(s^(7)+12)^((1/5)-1)*(7s^(6))
=(7s^(6)/5 ^(5)√(s^(7)+12)^4)

6.
Find the derivative of the function y=41e^(8t+1)

41e^(8t+1)*8
=328e^(8t+1)

7.
Find the derivative of the function w=e^(−6t)^2

e^(-6t)^(2)*(-6(2t))
=12te^(-6t)^2

8.
Find the derivative of the function f(x) = ln(27e^(14x)+6)