# Worksheet: The Quotient Rule

In this worksheet, we will practice finding the derivative of a function using the quotient rule.

Q1:

Find if .

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• B
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• D

Q2:

Find , given that .

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• D

Q3:

Find the first derivative of function .

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• B
• C
• D

Q4:

Differentiate .

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• C
• D

Q5:

Suppose and . Determine .

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• D

Q6:

Suppose that . Given that and , find and .

• A,
• B,
• C,
• D,

Q7:

Find the first derivative of .

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• C
• D
• E

Q8:

Find the first derivative of .

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• D

Q9:

Differentiate .

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• D

Q10:

Find the first derivative of the function .

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• D

Q11:

Given that , determine .

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• D

Q12:

Find the first derivative of with respect to .

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• D
• E

Q13:

If , find .

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• D

Q14:

If , find .

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• D

Q15:

Evaluate , where .

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• D

Q16:

Calculate , given .

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• D25

Q17:

Find the first derivative of the function .

• A
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• D

Q18:

Differentiate .

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• D

Q19:

Let . Given that , , , and , find .

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• D

Q20:

If , find .

Q21:

Find the values of for which , where .

• A6,
• B12,
• C36,

Q22:

Let . Use the definition of derivative to determine .

• A
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• D

Q23:

Find the derivative of the function , where , using the definition of derivative, and then state the domain of the function and the domain of its derivative.

• A, domain of function: , domain of derivative:
• B, domain of function: , domain of derivative:
• C, domain of function: , domain of derivative:
• D, domain of function: , domain of derivative:
• E, domain of function: , domain of derivative:

Q24:

Differentiate .

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• D
• E

Q25:

Evaluate , where .

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• C
• D