Free Printable Product and Quotient Differentiation

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Product and Quotient Differentiation

Total questions: 28

Worksheet time: 2hrs 55mins

Name

Class

Date

What is the derivative of f(x) = 2x³- 4x + 5?

f'(x) = 6x² - 4x

f'(x) = 2/3x² - 4x

f'(x) = 3x² - 4

f'(x) = 6x² - 4

Which function has the derivative of g'(x) = 4x³ + 2x - 1

g(x) = 2x⁴ + 2x² - 1

g(x) = x⁴ + x² - x

g(x) = 2x³ + x³ - 2x

g(x) = x⁵ + x² - x

At which point(s) will the slopes of the tangent line are zero?

at C only

at points A, C and E only

at point B and D only

at points A and E only

Let y = (x - 1)(x + 2). Find dy/dx.

2x + 1

2x - 1

4x - 1

2x² + x - 1

Let f(x) = (x - 1)(x + 2). Find f'(0)

At what point will the slope of y = -x² + 4 is zero?

(0, 4)

(1, 4)

(4, 0)

(1, 0)

What is the equation of the line tangent to the curve y = x² at x = 1?

y = 2x + 1

y = 2x - 1

y = -2x + 1

y = x - 1

What is the derivative of f?

1/(x - 1)^-1

-1/(x - 1)^-2

-1/(x - 1)

-1/(x - 1)²

What is the equation of the line tangent to the curve y = -x² + 3 at (1, 2)?

y = 2x - 4

y = -2x - 4

y = -2x + 4

y = 2x + 4

10.

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

m = 0

f'(x) = -6x - 6

f'(x) = 6x

m = -12

11.

Find the derivative of this function

(8x³ -60x/(2x²-5)²

16x⁴/(2x²-5)²

(8x⁴ -60x²)/(2x²-5)²

3x/(2x²-5)²

12.

Derivative means the same thing as

slope of the tangent line

slope of the normal line

exponent

potato

13.

How do you find horizontal tangent lines?

Find where the derivative is undefined

Find where the derivative equals zero

Find where the derivative is 1

Find where the derivative is negative

14.

What is the derivative for y=(x+1)(-2x+2) ?

-4x-2

-4x

-2x-2

-2x

15.

Find the derivative of y = 2x² (3x - 4)

6x³ - 8x²

18x² - 16x

15x²- 6x

6x - 4

16.

Find the derivative of g(x)=(3x-2)/(x²+2)

9x²+2

3(x²+2)/(x²+2)²

(-3x²+4x +6)/(x²+2)²

(-3x²+10)/(x²+2)²

17.

12x⁴ +3x²

20x⁴+3x² +16

3x⁵ +32x³ +6x² +8x

24x³

18.

Which if the following is not a correct notation for 'derivative?'

f'(x)

dy/dx

19.

Find the derivative.
y = 2 / (2x⁴ − 5)

y ′ = -16x³ / (2x⁴-5)

y′ = 4x⁶ + 8x³ + 4

y′ = 16x³

20.

-20x⁶ + 10x

-70x⁶ + 30x⁴ + 10x

5x² + 10x - 3

-10x⁷ - 94x⁵ + 5x² - 3

21.

What is the quotient rule for the derivative of f = u/v?

f' = (vu' - uv')/v²

f' = (uv' - vu')/v²

f' = (vu' - uv')/u²

f' = (uv' - vu')/u²

22.

Find f'(x) if
f(x)=(2x-7)/(x+3)

13/(x+3)²

-4/(x+3)²

-13/(x+3)

23.

Find the derivative: h(x)=(3x+2)(5x³+2x)

60x³+30x +12x-4

60x³-30x²+12x-4

45x³+30x²+12x+4

60x³+30x²+12x+4

24.

Let y = (x - 1)(x + 2). Find dy/dx.

2x + 1

2x - 1

4x - 1

2x² + x - 1

25.

Given u = fg, f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,
then u'(2) = ?

-12

26.

Given v = f/g, f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,
then v'(2) = ?

-2

nine fifths

negative four thirds

27.

At which x-value is f continuous but not differentiable?

28.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

(12x³)*(10x)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

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Product and Quotient Differentiation

Total questions: 28

Worksheet time: 2hrs 55mins

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