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Find the derivative. 1) y = 7e^-11x

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 =e6x^2 + x

A) 12xe2x + 1

B) 12xe6x^2 + 1

C) 12xe + 1

D) 12xex^2 + 1

3) y = 4ex^2

A) 8xex^2

B) 8xe2x

C) 8xe4x^2

D) 8xe

4) y = 4ex^2

A) 8xe4x^2

B) 8xe

C) 8xex^2

D) 8xe2x

5) y = (3ex/2ex + 1)

A) (3ex/(2ex + 1))

B) (3ex/(2ex + 1)2)

C) (3ex/(2ex + 1)3)

D) (ex/(2ex + 1)2)

6) y = 5x2e3x

A) 10xe3x(2x + 3)

B) 10ex^3x(3x + 2)

C) 5xe3x(3x + 2)

D) 5xe3x(2x + 3)

7) y = (e-x + 1/ex)

A) (ex + 2/e2x)

B) (ex - 2/e2x)

C) (-ex - 2/e2x)

D) (-ex + 2/e2x)

8) y = (100/2 + 9e3x)

A) (200 + 630e3x/(2 + 9e3x)2)

B) (270e3x/(2 + 9e3x)2)

C) (200 + 1170e3x/(2 + 9e3x)2)

D) (-270e3x/(2 + 9e3x)2)

9) y = (x + 4)4e-5x

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

B) -20(x + 4)3e-5x

C) -(x + 4)3(5x + 16)e-5x

D) (x + 4)3(x + 8)e-5x

10) y = (ex/6x2 + 9)

A) (ex-1(6x2 + 9) - 12xex/(6x2 +9)2)

B) (ex(6x2 - 12x + 9)/(6x2 + 9)2)

C)ex + (6x2 - 12x + 9/(6x2 + 9)2)

D) (ex-1(6x2 - 12x + 9)/(6x2 + 9)2)

11) y = 210x

A) 20(ln10)210x

B) 2(ln10)210x

C) 10(ln2)210x

D) 20(ln2)210x

12) y = 20-x

A) 20-x

B) ln20(20-x)

C) -20-x

D) -ln20(20-x)

13) y = 5(66x - 3) - 7

A) 30ln30 (66x - 3)

B) 30ln6 (66x - 3)

C) 36ln6 (66x - 3)

D) 36ln30 (66x - 3)

14) y = 2(5√(x))

A) ln5(5√(x))(√(x))

B) (ln5(5√(x))/√(x))

C) (2ln5(5x)/√(x))

D) 2ln5(5√(x))(√(x))

15) y = 18x - 1

A) 18x - 1ln18

B) 18x - 1lnx

C) 18x - 1ln18x - 1

D) 18ln18

16) y = 11x2

A) 11x2xln11

B) 11x22xlnx

C) 11x22xln11

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(e2.6t -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 N0 (in grams) is given by N = N0(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) = 12t2e-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) = Po(1 -e-kt), where D(t) is the number of daughters, Po is the initial number of parent atoms, k is the decay rate constant in units of s-1, and t is in seconds. Find anexpression for the rate of change of D with respect to time.

A) D'(t) = kPoe-kt

B) D'(t) = Po + Poe-kt

C) D'(t) = kPoe-kt - 1

D) D'(t) = -kPoe-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)

Solution
5 (1 Ratings )

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