# Worksheet: Definition of the Derivative

In this worksheet, we will practice calculating the derivative of a function using the formal definition of the derivative as a limit.

**Q5: **

Determine the derivative of the function using the definition of the derivative.

- A
- B
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- D

**Q7: **

Given a function with and , what is ?

- A
- B15
- C
- D0
- E3

**Q8: **

Consider a function with and . What is ?

**Q9: **

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

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q10: **

Let . Use the definition of derivative to determine .

- A
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- D

**Q11: **

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

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q13: **

Find the derivative of at the point from first principles.

**Q14: **

Find the derivative of the function using the definition of the derivative.

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- D
- E

**Q15: **

Find the derivative of the function using the definition of the derivative.

- A
- B
- C
- D
- E

**Q16: **

Find the derivative of the function using the definition of the derivative.

- A
- B
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- D
- E

Find the equation of the tangent to the graph of at .

- A
- B
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- D
- E

**Q17: **

Find the derivative of the function using the definition of the derivative.

- A
- B
- C
- D
- E

**Q18: **

Find the derivative of the function using the definition of the derivative.

- A
- B
- C
- D
- E