# Worksheet: Combining the Product, Quotient, and Chain Rules

In this worksheet, we will practice finding the first derivative of a function using combinations of the product, quotient, and chain rules.

**Q3: **

Differentiate , where and are two constants.

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**Q4: **

Find , given that .

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**Q5: **

Find the first derivative of the function .

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**Q6: **

Find the first derivative of the function .

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**Q7: **

Find the first derivative of the function .

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**Q8: **

Find the first derivative of the function .

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**Q9: **

Differentiate .

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**Q10: **

Let . If and , find .

**Q11: **

If , find .

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**Q12: **

Find the first derivative of the function .

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**Q13: **

Evaluate .

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**Q14: **

Differentiate , and identify the value of at which the function is NOT differentiable.

- A , the function is not differentiable at .
- B , the function is not differentiable at .
- C , the function is not differentiable at .
- D , the function is not differentiable at .

**Q15: **

Find , given that .

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**Q16: **

Find the first derivative of with respect to .

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**Q17: **

Evaluate .

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**Q18: **

Differentiate .

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**Q19: **

If , which of the following is the same as ?

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**Q20: **

Find .

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**Q21: **

Find the first derivative of the function .

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**Q22: **

Differentiate .

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**Q23: **

Find , given that .

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**Q24: **

Differentiate .

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**Q25: **

If , find .

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