# 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 .

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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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Q8:

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

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Q9:

Suppose that , , , and . Evaluate at .

Q10:

Find the first derivative of .

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Q11:

Suppose that and . Determine .

Q12:

Find the first derivative of the function .

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Q13:

Find the first derivative of the function .

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Q14:

Find the first derivative of the function .

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Q15:

Find the first derivative of the function .

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Q16:

Consider the functions , .

Find and .

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Find .

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Given that , find its derivative.

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