#
Question : Find the derivative. 1) y = 7e^-11x : 2151684

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the derivative.

1) y = 7e^{-11x}

A) -77xe^{-11x}

B) -77e^{-11x}

C) 7xe^{-77x}

D) 7e^{-77x}

2) y =e^{6x^2} + x

A) 12xe^{2x} + 1

B) 12xe^{6x^2} + 1

C) 12xe + 1

D) 12xe^{x^2} + 1

3) y = 4e^{x^2}

A) 8xe^{x^2}

B) 8xe^{2x}

C) 8xe^{4x^2}

D) 8xe

4) y = 4e^{x^2}

A) 8xe^{4x^2}

B) 8xe

C) 8xe^{x^2}

D) 8xe^{2x}

5) y = (3e^{x}/2e^{x} + 1)

A) (3e^{x}/(2e^{x} + 1))

B) (3e^{x}/(2e^{x} + 1)^{2})

C) (3e^{x}/(2e^{x} + 1)^{3})

D) (e^{x}/(2e^{x} + 1)^{2})

6) y = 5x^{2}e^{3x}

A) 10xe^{3x}(2x + 3)

B) 10e^{x^3x}(3x + 2)

C) 5xe^{3x}(3x + 2)

D) 5xe^{3x}(2x + 3)

7) y = (e^{-x} + 1/e^{x})

A) (e^{x} + 2/e^{2x})

B) (e^{x} - 2/e^{2x})

C) (-e^{x} - 2/e^{2x})

D) (-e^{x} + 2/e^{2x})

8) y = (100/2 + 9e^{3x})

A) (200 + 630e^{3x}/(2 + 9e^{3x})^{2})

B) (270e^{3x}/(2 + 9e^{3x})^{2})

C) (200 + 1170e^{3x}/(2 + 9e^{3x})^{2})

D) (-270e^{3x}/(2 + 9e^{3x})^{2})

9) y = (x + 4)^{4}e^{-5x}

A) -(x + 4)^{3}(5x + 16)e^{-6x}

B) -20(x + 4)^{3}e^{-5x}

C) -(x + 4)^{3}(5x + 16)e^{-5x}

D) (x + 4)^{3}(x + 8)e^{-5x}

10) y = (e^{x}/6x^{2} + 9)

A) (e^{x-1}(6x^{2} + 9) - 12xe^{x}/(6x^{2} +9)^{2})

B) (e^{x}(6x^{2} - 12x + 9)/(6x^{2} + 9)^{2})

C)e^{x} + (6x^{2} - 12x + 9/(6x^{2} + 9)^{2})

D) (e^{x-1}(6x^{2} - 12x + 9)/(6x^{2} + 9)^{2})

11) y = 2^{10x}

A) 20(ln10)2^{10x}

B) 2(ln10)2^{10x}

C) 10(ln2)2^{10x}

D) 20(ln2)2^{10x}

12) y = 20^{-x}

A) 20^{-x}

B) ln20(20^{-x})

C) -20^{-x}

D) -ln20(20^{-x})

13) y = 5(6^{6x - 3}) - 7

A) 30ln30 (6^{6x - 3})

B) 30ln6 (6^{6x - 3})

C) 36ln6 (6^{6x - 3})

D) 36ln30 (6^{6x - 3})

14) y = 2(5^{√(x)})

A) ln5(5^{√(x)})(√(x))

B) (ln5(5^{√(x)})/√(x))

C) (2ln5(5^{x})/√(x))

D) 2ln5(5^{√(x)})(√(x))

15) y = 18x - 1

A) 18x - 1ln18

B) 18x - 1lnx

C) 18x - 1ln18x - 1

D) 18ln18

16) y = 11x^{2}

A) 11x^{2}xln11

B) 11x^{2}2xlnx

C) 11x^{2}2xln11

D) 2xln11

Solve the problem.

17) The sales in thousands of a new type of product are given by S(t) = 300 - 20e^{-0.5t}, where t represents time in years. Find the rate of change of sales at the time when t = 7.

A) -327.6 thousand per year

B) 327.6 thousand per year

C) 0.3 thousand per year

D) -0.3 thousand per year

18) A company's total cost, in millions of dollars, is given by C(t) = 180 - 60e^{-t} where t = time in years. Find the marginal cost when t = 2.

A) 5.97 million dollars per year

B) 8.12 million dollars per year

C) 16.24 million dollars per year

D) 24.36 million dollars per year

19) The demand function for a certain book is given by the function x = D(p) = 62e^{-0.006p}. Find the marginal demand D'(p).

A) D'(p) = -0.006e^{-0.006p}

B) D'(p) = 0.372e^{-0.006p}

C) D'(p) = -0.372e^{-0.006p}

D) D'(p) = -0.372pe^{-0.006p-1}

20) Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t) = 540e^{-0.60t}. Find the rate of change of the quantity present at the time when t = 2.

A) 97.6 grams per year

B) -3.3 grams per year

C) -97.6 grams per year

D) 3.3 grams per year

21) When a particular circuit containing a resistor, an inductor, and a capacitor in series is connected to a battery, the current i (in amperes) is given by i = 27e^{-3t}(e^{2.6t} -e^{-2.6t}) where t is the time (in seconds). Find the time at which the maximum current occurs. Round to the nearest tenth of a second.

A) 0.5 sec

B) 1.4 sec

C) 0.6 sec

D) 1.5 sec

22) When a radioactive substance decays, the number N of grams remaining from an initial mass N_{0} (in grams) is given by N = N_{0}(1/2)^{n}, where n is the number of half-lives for which the substance has decayed. Given that the half-life for tritium is 12 years, find the rate in (grams/half-life) at which a 111-gram initial mass of radioactive tritium decays after 38.4 years.

A) -12.08 g/half-life

B) -76.93 g/half-life

C) -8.37 g/half-life

D) -2.9 g/half-life

23) The nationwide attendance per day for a certain motion picture can be approximated using theequation A(t) = 12t^{2}e^{-t}, where A is the attendance per day in thousands of persons and t is the number of months since the release of the film. Find and interpret the rate of change of the daily attendance after 4 months.

A) 3.517 thousand persons/day ? month; the daily attendance is increasing.

B) -1.758 thousand persons/day ? month; the daily attendance is decreasing.

C) -3.517 thousand persons/day ? month; the change in daily attendance is decreasing.

D) 1.758 thousand persons/day ? month; the change in the daily attendance is increasing.

24) As a radioactive sample disintegrates, the "parent" atoms are converted into "daughter" atoms. The number of daughter atoms D(t) that have been formed by a particular time t is given by D(t) = P_{o}(1 -e^{-kt}), where D(t) is the number of daughters, P_{o} is the initial number of parent atoms, k is the decay rate constant in units of s^{-1}, and t is in seconds. Find ane^{x}pression for the rate of change of D with respect to time.

A) D'(t) = kP_{o}e^{-kt}

B) D'(t) = P_{o} + P_{o}e^{-kt}

C) D'(t) = kP_{o}e^{-kt - 1}

D) D'(t) = -kP_{o}e^{-kt}

25) In one city, 34% of all aluminum cans distributed will be recycledeach year. A juice company distributes 293,000 cans. The number still in use after time t, in years, is given by

N(t) = 293,000(0.34)^{t}.

Find N'(t).

A) N'(t) = 293,000(ln0.34)(0.34)^{t}

B) N'(t) = 293,000t(0.34)^{t-1}

C) N'(t) = 293,000(lnt)(0.34)^{t}

D) N'(t) = 293,000(0.34)^{t}

26) The pH scale is used by chemists to measure the acidity of a solution. It is a base 10 logarithmic scale. The pH, P, of a solution and its hydronium ion concentration in moles per liter, H, are related as follows:

H = 10^{-P}

Find the formula for the rate of change (dH/dP).

A) (dH/dP) = -(lnP)10^{-P}

B) (dH/dP) = -(ln10)10^{-P}

C) (dH/dP) = (ln10)10^{-P}

D) (dH/dP) = - (10^{-P}/ln10)