# 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
- C
- D

**Q6: **

Evaluate .

- A
- B
- C
- D
- E

**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
- B
- C
- 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 , ,

**Q12: **

Consider the function .

Find .

Find .

What can you conclude about the derivative of at ?

- ASince the right and left limits are unequal, the derivative does not exist.
- BThe derivative exists and is equal to .
- CThe derivative exists and is equal to 1.
- DThe derivative exists and is equal to 0.

**Q13: **

Find the derivative of at the point from first principles.