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Find the derivative of the function. 1) y = ln4x

Question : Find the derivative of the function. 1) y = ln4x : 2151691

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

Find the derivative of the function.

1) y = ln4x

A) - (1/x)

B) (1/4x)

C) - (1/4x)

D) (1/x)

2) y = ln(x - 3)

A) (1/x + 3)

B) (1/x - 3)

C) - (1/x + 3)

D) (1/3 - x)

3) y = ln5x2

A) (10/x)

B) (2x/x2 + 5)

C) (1/2x + 5)

D) (2/x)

4) y = ln(6 + x2)

A) (12/x)

B) (2x/x2 + 6)

C) (2/x)

D) (1/2x + 6)

5) y = ln|6x3 - x2|

A) (18x - 2/6x2)

B) (6x - 2/6x2 - x)

C) (18x - 2/6x2 - x)

D) (18x - 2/6x3 - x)

6) y = x2lnx2

A) 2x +lnx2

B) (2x2 + 2/x)

C) 2x(1 +lnx2)

D) (2x2(1 +lnx2)/x)

7) y = ln(x + 9)5

A) (5/x)

B) (5/x + 9)

C) (9/x + 9)

D) (5/x + 5)

8) y = (5x2/ln|3x|)

A) (5xln|3x| - 10x/(ln|3x|)2)

B) (10xln|3x| - 5x/(ln|3x|)2)

C) (ln|3x| - 10x/(ln|3x|)2)

D) (ln|3x| - 5x/(ln|3x|)2)

9) y = (4x2 + 10)ln(x + 8)

A) 8xln(x + 8)

B) (8x/x + 8)

C) (4x2 + 10/x + 8) + 8xln(x + 8)

D) (4x2 + 10/ln(x + 8)) + 8xln(x + 8)

10) y = (4ln(x + 4)/7 - 6x)

A) (28 + 24x + 24(x + 4)ln(x + 4)/(x - 4)(7 - 6x)2)

B) (4/(x + 4)(7 - 6x)2)

C) (28 - 24x + 24ln(x + 4)/(x + 4)(7 - 6x))

D) (28 - 24x + 24(x + 4)ln(x + 4)/(x + 4)(7 - 6x)2)

Find the derivative.

11) y = exlnx, x > 0

A) exlnx

B) (ex(lnx + x)/x)

C) (ex(xlnx + 1)/x)

D) (ex/x)

12) y = (ex/lnx)

A) (ex - xexlnx/xln2x)

B) (xexlnx - ex/xln2x)

C) (ex + xexlnx/x)

D) xex

13) y = ex5lnx

A) (ex5 + 5x4ex5lnx/x)

B) (ex5 + 5x5ex5lnx/x)

C) (ex5 + 5ex5lnx/x)

D) (5x5ex5 + 1/x)

14) y = (ln(9x + 4)/e9x + 4)

A) (1 - (9x + 4)ln(9x + 4)/(9x + 4)e(9x + 4))

B) (9 - (81x + 36)ln(9x + 4)/(9x + 4)e(9x + 4))

C) (1 - 9 [ln(9x + 4)]2/ln[9x + 4]e(9x + 4))

D) (1/(9x + 4)e(9x + 4))

Find the derivative of the function.

15) y = log(3x)

A) (1/x(ln3))

B) (1/x)

C) (1/x(ln10))

D) (1/ln10)

16) y = log(7x - 1)

A) (7/ln10)

B) (7x - 1/7ln10)

C) (7/ln10 (7x - 1))

D) (1/ln10 (7x - 1))

17) y = log|8 - x|

A) - (1/ln10)

B) (1/ln10 (8 - x))

C) - (8 - x/ln10)

D) - (1/ln10 (8 - x))

18) y = log|-4x|

A) - (1/x (ln10))

B) - (ln10/x)

C) (x/ln10)

D) (1/x(ln10))

19) y = log6√(9x + 3)

A) (9/ln6)

B) (9ln6/9x + 3)

C) (9/2(ln6)(9x + 3))

D) (9/ln6(9x + 3))

20) y = log4|(3x2 - 2x)5/2|

A) (10(3x - 1)/ln4(3x2 - 2x))

B) (ln4(3x - 1)/(3x2 - 2x))

C) (5(3x - 1)/ln4(3x2 - 2x))

D) (5/ln4(3x2 - 2x))

Solve the problem.

21) Assume the total revenue from the sale of x items is given by R(x) = 28ln(5x + 1), while the total cost to produce x items is C(x) = x/2. Find the approximate number of items that should be manufactured so that profit, R(x) - C(x), is maximum.

A) 56 items

B) 70 items

C) 99 items

D) 142 items

22) Suppose that the population of a certain type of insect in a region near theequator is given by P(t) = 18ln(t + 12), where t represents the time in days. Find the rate of change of the population when t = 4.

A) 2.4 insects

B) 1.5 insects

C) 4.5 insects

D) 1.1 insects

23) Suppose that the demand function for x units of a certain item is p = 110 + (210ln(x + 5)/x), where p is the price per unit, in dollars. Find the marginal revenue.

A) (dR/dx) = (210 [x - (x + 5)ln(x + 5)]/x2(x + 5))

B) (dR/dx) = 110 + (210/ln(x + 5))

C) (dR/dx) = (210[x - [ln(x + 5) ]2]/x2ln(x + 5))

D) (dR/dx) = 110 + (210/x + 5)

24) The population of coyotes in the northwestern portion of Alabama is given by the formula p(t) = (t2 + 100)ln(t + 2) , where t represents the time in years since 2000 (the year 2000 corresponds to t = 0). Find the rate of change of the coyote population in 2011(t = 11).

A) 17 coyotes/year

B) 73 coyotes/year

C) 56 coyotes/year

D) 143 coyotes/year

25) Students in a math class took a finalexam. They tookequivalent forms of theexam in monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by

S(t) = 79 - 17ln(t + 1), t ≥ 0.

Find S'(t).

A) S'(t) = (17/t + 1)

B) S'(t) = - (17/t + 1)

C) S'(t) = 79 - (17/t + 1)

D) S'(t) = - 17ln((1/t + 1))

26) Suppose that the population of a town is given by

P(t) = 4ln√(4t + 9),

where t is the time in years after 1980 and P is the population of the town in thousands. Find P'(t).

A) P'(t) = (2/4t + 9)

B) P'(t) = (8/4t + 9)

C) P'(t) = (4/√(4t + 9))

D) P'(t) = (8ln√(4t + 9)/√(4t + 9))

Solution
5 (1 Ratings )

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Calculus 3 Months Ago 25 Views
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