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Quotient Rule Practice Worksheet

Practice problems for applying the quotient rule in calculus to find derivatives of functions.

Grade 9 Math CalculusQuotient Rule
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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.ECCSS.MATH.CONTENT.HSF.BF.B.3
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Quotient Rule Practice Worksheet

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Read each question carefully and apply the quotient rule to find the derivative of the given functions. Show all your work.

1. Find the derivative of the function f(x) = (3x - 1) / (x^2 + 1).

2. Differentiate the function g(x) = sin(x) / cos(x).

3. Determine the derivative of h(x) = (e^x) / (x^3).

The Quotient Rule states that if f(x) = g(x) / h(x), then f'(x) = (h(x) * g'(x) - g(x) * h'(x)) / ( ).

1. Which of the following is the correct application of the quotient rule for y = u/v?

a

y' = (vu' + uv') / v^2

b

y' = (vu' - uv') / v^2

c

y' = (uv' - vu') / v^2

d

y' = (uv' + vu') / v^2

1. The quotient rule is only applicable when both the numerator and denominator are differentiable functions.

T

True

F

False

1. Find the derivative of the function y = (x^2 + 2x - 3) / (x^3 - 4x).