# Worksheet: Differentiation of Inverse Functions

In this worksheet, we will practice finding the derivatives of inverse functions.

Q1:

Use the graph of to estimate . • A
• B
• C
• D
• E2

Q2:

Use the inverse function theorem to find the derivative of .

• A
• B
• C
• D
• E

Q3:

Consider the function and .

Find the slope of the tangent line to its inverse function at the indicated point .

• A
• B4
• C
• D1
• E2

Find the equation of the tangent line to the graph of at the indicated point .

• A
• B
• C
• D
• E

Q4:

A wall is 15 feet high. An angle is formed when a ladder of length is placed against the wall such that the top of the ladder is at the top of the wall, as shown in the figure. The ladder's length can be changed, but the top of the ladder always remains at the top of the wall. Find the rate of change, to the nearest ten thousandth, of the angle when the ladder has a length of 21 feet. Q5:

If , , and , find .

Q6:

If , , and , find .

• A
• B3
• C2
• D
• E

Q7:

For the function at , find .

• A
• B
• C
• D5
• E0

Q8:

For the function at , find .

• A14
• B12
• C
• D2
• E

Q9:

For the function at , , find .

• A3
• B
• C
• D
• E0

Q10:

For the function at , , find .

• A
• B2
• C
• D3
• E

Q11:

Consider the function and .

Find the slope of the tangent line to its inverse function at the indicated point .

• A365
• B14
• C
• D11
• E

Find the equation of the tangent line to the graph of at the indicated point .

• A
• B
• C
• D
• E

Q12:

Use the inverse function theorem to find the derivative of .

• A
• B
• C
• D
• E

Q13:

If , , and , find .

Q14:

For the function at , find .

• A
• B
• C14
• D
• E4

Q15:

Let be the inverse of . Using the values in the table, find .

59
030

Q16:

Let be the inverse of . Using the values in the table, find .

𝑥 𝑓(𝑥) 1 2 −5 −9 2 4 −2 1

Q17:

Given that , find .

• A
• B
• C
• D
• E

Q18:

Given that , find , giving your answer in terms of .

• A
• B
• C
• D
• E

Q19:

Consider the function , where .

Find .

• A0
• B
• C
• D
• E

Express in terms of .

• A
• B
• C
• D
• E

By expressing in terms of , find an expression for .

• A
• B
• C
• D
• E

Q20:

Let and let be the inverse of . Given that , what is ?

• A
• B
• C
• D
• E

Q21:

Given that , find .

• A
• B
• C
• D
• E

Q22:

Let and let be the inverse of . Given that , what is ?

• A
• B233
• C
• D
• E13