# Worksheet: Higher-Order Derivatives

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:

If , find .

Q5:

True or False: .

• Afalse
• Btrue

Q6:

Given , find .

• A
• B
• C
• D

Q7:

Given that , and , determine .

Q8:

Find given .

Q9:

If , and , find .

• A
• B
• C
• D

Q10:

Given that , determine .

• A
• B
• C
• D
• E

Q11:

Find the third derivative of the function .

• A
• B
• C
• D

Q12:

Find the first and second derivatives of the function .

• A ,
• B ,
• C ,
• D ,
• E ,

Q13:

Given that , find at .

• A8
• B0
• C
• D

Q14:

Given that , determine .

• A
• B
• C
• D

Q15:

Find the third derivative of the function .

• A
• B
• C
• D

Q16:

Given that , determine .

• A
• B
• C
• D

Q17:

Find the second derivative of the function at the point .

Q18:

Given and . Find the value of .

• A
• B
• C6
• D

Q19:

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

• A
• B
• C
• D
• E

Q20:

If , find .

• A
• B
• C
• D

Q21:

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

• A16
• B48
• C
• D

Q22:

Evaluate .

• A
• B
• C
• D

Q23:

Given that , determine .

• A
• B
• C
• D
• E

Q24:

If , find .

• A
• B
• C
• D

Q25:

Given that , determine .

• A
• B
• C
• D