# Lesson Worksheet: Definition of the Derivative Mathematics • Higher Education

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

**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, ,

**Q14: **

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
- C
- D
- E

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

- A
- B
- C
- 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

**Q19: **

Suppose . If the average rate of change as changes from 3 to 3.5 is 4 and , determine and .

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

**Q20: **

What is the rate of change of with respect to at ?

**Q21: **

Consider the function .

Find and .

What can you conclude about the derivative of at ?

- AThe derivative exists and is equal to 2.
- BSince the right and left limits are unequal, the derivative does not exist.
- CThe derivative exists and is equal to .
- DThe derivative exists and is equal to .
- EThe derivative exists and is equal to .

**Q22: **

What is the slope of the tangent to at ?

- A
- B
- C
- D
- ENone of the above

**Q23: **

Find .

- Aundefined
- B
- C
- D
- E

**Q25: **

If , find .