# Worksheet: Second- and Higher-Order Derivatives

In this worksheet, we will practice finding second- and higher-order derivatives of a function including using differentiation rules.

Q1:

Find the first and second derivatives of the function .

• A,
• B,
• C,
• D,
• E,

Q2:

Given that , , and , find and .

• A,
• B,
• C,
• D,

Q3:

Find the third derivative of the function .

• A
• B
• C
• D
• E

Q4:

Given , find .

• A
• B
• C
• D

Q5:

Given that , and , determine .

Q6:

If , and , find .

• A
• B
• C
• D

Q7:

Determine the value of the second derivative of the function at .

Q8:

If , find .

Q9:

Given that , determine .

• A
• B
• C
• D
• E

Q10:

Find the third derivative of the function .

• A
• B
• C
• D

Q11:

Find the first and second derivatives of the function .

• A,
• B,
• C,
• D,
• E,

Q12:

Given that , find at .

• A0
• B8
• C
• D

Q13:

Given that , determine .

• A
• B
• C
• D

Q14:

Find the third derivative of the function .

• A
• B
• C
• D

Q15:

Given that , determine .

• A
• B
• C
• D

Q16:

Find the second derivative of the function at the point .

Q17:

Given and . Find the value of .

• A
• B
• C
• D6

Q18:

Find by finding the first few derivatives and observing the pattern that occurs.

• A
• B
• C
• D
• E

Q19:

If , find .

• A
• B
• C
• D

Q20:

Evaluate .

• A
• B
• C
• D

Q21:

Given that , determine .

• A
• B
• C
• D
• E

Q22:

If , find .

• A
• B
• C
• D

Q23:

Given that , determine .

• A
• B
• C
• D

Q24:

Determine the second derivative of the function at .

• A
• B
• C
• D

Q25:

Find the third derivative of the function .

• A
• B
• C
• D
• E