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Use the product rule to find the derivative. 1) f(x) = (2x - 2)(4x + 1)
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# Question : Use the product rule to find the derivative. 1) f(x) = (2x - 2)(4x + 1) : 2151598

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

Use the product rule to find the derivative.

1) f(x) = (2x - 2)(4x + 1)

A) f'(x) = 16x - 10

B) f'(x) = 8x - 6

C) f'(x) = 16x - 3

D) f'(x) = 16x - 6

2) f(x) = (3x - 2)(2x3 - x2 + 1)

A) f'(x) = 24x3 - 21x2 + 4x + 3

B) f'(x) = 6x3 + 7x2 - 21x + 3

C) f'(x) = 18x3 + 21x2 - 7x + 3

D) f'(x) = 24x3 - 7x2 + 21x + 3

3) f(x) = (x2 - 4x + 2)(2x3 - x2 + 5)

A) f'(x) = 10x4 - 32x3 + 24x2 + 6x - 20

B) f'(x) = 10x4 - 36x3 + 24x2 + 6x - 20

C) f'(x) = 2x4 - 36x3 + 24x2 + 6x - 20

D) f'(x) = 2x4 - 32x3 + 24x2 + 6x - 20

4) f(x) = (4x + 3)2

A) f'(x) = 16x + 12

B) f'(x) = 8x + 6

C) f'(x) = 32x + 24

D) f'(x) = 16x + 9

5) f(x) = (5x - 4)(√(x) + 2)

A) f'(x) = 3.33x1/2 - 4x-1/2 + 10

B) f'(x) = 3.33x1/2 - 2x-1/2 + 10

C) f'(x) = 7.5x1/2 - 4x-1/2 + 10

D) f'(x) = 7.5x1/2 - 2x-1/2 + 10

6) f(x) = (5x3 + 6)(5x7 - 8)

A) f'(x) = 250x9 + 210x6 - 120x2

B) f'(x) = 250x9 + 210x6 - 120x

C) f'(x) = 20x9 + 210x6 - 120x2

D) f'(x) = 20x9 + 210x6 - 120x

7) f(x) = (6√(x) - 2)(5√(x) + 7)

A) f'(x) = 30 + 32x-1/2

B) f'(x) = 30x + 16x1/2

C) f'(x) = 30 + 16x-1/2

D) f'(x) = 30x + 32x1/2

8) g(x) = (x-5 + 3)(x-3 + 5)

A) g'(x) = -8x-9 - 25x-6 - 9x-2

B) g'(x) = -8x-9 - 25x-4 - 9x-4

C) g'(x) = -8x-9 - 25x-6 - 9x-4

D) g'(x) = -8x-7 - 25x-6 - 9x-4

9) f(x) = (3x4 + 8)2

A) f'(x) = 6x4 + 16

B) f'(x) = 144x15 + 96x3

C) f'(x) = 9x16 + 64

D) f'(x) = 72x7 + 192x3

10) (y-2 + y-1)(6y-3 - 7y-4)

A) (42 + 4y - 6y2/y7)

B) (42 - 5y + 24y2/y7)

C) (42 + 65y - 24y2/y7)

D) (42 + 5y - 24y2/y7)

Use the quotient rule to find the derivative.

11) f(x) = (1/x7 + 2)

A) f'(x) = (1/(7x7 + 2)2)

B) f'(x) = (7x6/(x7 + 2)2)

C) f'(x) = - (1/(7x7 + 2)2)

D) f'(x) = - (7x6/(x7 + 2)2)

12) g(t) = (t2/t - 11)

A) g'(t) = (t2/(t - 11)2)

B) g'(t) = (t2 + 22t/(t - 11)2)

C) g'(t) = (t2 - 22t/(t - 11)2)

D) g'(t) = (22t/(t - 11)2)

13) y = (x2 - 3x + 2/x7 - 2)

A) (dy/dx) = (-5x8 + 18x7 - 14x6 - 4x + 6/(x7 - 2)2)

B) (dy/dx) = (-5x8 + 18x7 - 14x6 - 3x + 6/(x7 - 2)2)

C) (dy/dx) = (-5x8 + 18x7 - 13x6 - 4x + 6/(x7 - 2)2)

D) (dy/dx) = (-5x8 + 19x7 - 14x6 - 4x + 6/(x7 - 2)2)

14) y = (x3/x - 1)

A) (dy/dx) = (-2x3 - 3x2/(x - 1)2)

B) (dy/dx) = (2x3 - 3x2/(x - 1)2)

C) (dy/dx) = (-2x3 + 3x2/(x - 1)2)

D) (dy/dx) = (2x3 + 3x2/(x - 1)2)

15) g(x) = (x2 + 5/x2 + 6x)

A) g'(x) = (6x2 - 10x - 30/x2(x + 6)2)

B) g'(x) = (4x3 + 18x2 + 10x + 30/x2(x + 6)2)

C) g'(x) = (2x3 - 5x2 - 30x/x2(x + 6)2)

D) g'(x) = (x4 + 6x3 + 5x2 + 30x/x2(x + 6)2)

16) y = (x2 - 4/x)

A) (dy/dx) = 1 + (4/x)

B) (dy/dx) = 1 + (4/x2)

C) (dy/dx) = x + (4/x2)

D) (dy/dx) = 1 - (4/x2)

17) y = (x2 + 8x + 3/√(x))

A) (dy/dx) = (3x2 + 8x - 3/x)

B) (dy/dx) = (3x2 + 8x - 3/2x3/2)

C) (dy/dx) = (2x + 8/2x3/2)

D) (dy/dx) = (2x + 8/x)

18) y = (x2 + 2x - 2/x2 - 2x + 2)

A) (dy/dx) = (4x2 - 8x/(x2 - 2x + 2)2)

B) (dy/dx) = (4x2 + 8x/(x2 - 2x + 2)2)

C) (dy/dx) = (-4x2 + 8x/(x2 - 2x + 2)2)

D) (dy/dx) = (-4x2 - 8x/(x2 - 2x + 2)2)

19) f(x) = (x2.5 + 4/x2.9 + 1)

A) f'(x) = (-0.4x4.4 + 2.5x1.5 - 2.9x2.5 + 4x1.9 - 11.6/(x2.9 + 1)2)

B) f'(x) = (-0.4x4.4 + 2.5x1.5 - 2.9x2.5 - 11.6x1.9 - 11.6/x2.9 + 1)

C) f'(x) = (-0.4x4.4 - 0.4x2.5 - 11.6x1.9 - 11.6/(x2.9 + 1)2)

D) f'(x) = (-0.4x4.4 + 2.5x1.5 - 11.6x1.9/(x2.9 + 1)2)

20) f(x) = ((4x - 1)(4x2 + 1)/5x + 2)

A) f'(x) = (160x3 + 76x2 - 16x + 13/5x + 2)

B) f'(x) = (160x3 + 76x2 - 16x + 13/(5x + 2)2)

C) f'(x) = (160x3 + 96x2 - 16x + 13/(5x + 2)2)

D) f'(x) = (80x3 + 76x2 + 16x + 13/(5x + 2)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.

21) f(x) = (-5x2 - 5x - 4)(2x - 5), x = 0

A) y = 17x + 20

B) y = 17x - 20

C) y = (1/17)x - 20

D) y = (1/17)x + 20

22) f(x) = (3x2 - 9/-4x - 3), x = 0

A) y = 4x - 3

B) y = 4x + 3

C) y = - 4x - 3

D) y = - 4x + 3

Using a graphing calculator, find the values of x for which f'(x) = 0, to three decimal places.

23) f(x) = (5 - x2)(x2 - √(5))

A) 0, -1.393, 1.393

B) 0, -1.902, 1.902

C) 0

D) There are no real values of x for which f'(x) = 0.

24) f(x) = (x2 - 4/x4 + 3)

A) -2.828, 2.828

B) 0, -2.891, 2.891

C) 0

D) There are no real values of x for which f'(x) = 0.

## Solution 5 (1 Ratings )

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Calculus 3 Months Ago 25 Views