# Worksheet: The Product Rule

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

Q1:

Find at when .

Q2:

Find the first derivative of at .

Q3:

Find the first derivative of at .

Q4:

Find the first derivative of the function .

• A
• B
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• D

Q5:

Find the first derivative of at .

Q6:

Let . If , , , and , find .

Q7:

Suppose that is differentiable. What is the derivative of ?

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• E

Q8:

The product rule says that . Use this to derive a formula for the derivative .

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• E

Q9:

Suppose that , , , and . Evaluate at .

Q10:

Find the first derivative of .

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• D

Q11:

Suppose that and . Determine .

Q12:

Find the first derivative of the function .

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• E

Q13:

Find the first derivative of the function .

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• D

Q14:

Find the first derivative of the function .

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• D

Q15:

Find the first derivative of the function .

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• D

Q16:

Consider the functions , .

Find and .

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• D,

Find .

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Given that , find its derivative.

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Q17:

.

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Q18:

If , , and , then .

• A46
• B42
• C6
• D30

Q19:

If the function is an odd function and differentiable on and , then .

• A
• B12
• C
• D

Q20:

at .

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• D9

Q21:

If , then at .

• A
• B21
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• D45

Q22:

If is differentiable at , , , , then .

• A16
• B2
• C18
• D14

Q23:

If , then at .

• A7
• B
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• D

Q24:

.

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• D

Q25:

.

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• D