Cracking The Ap Calculus ab Exam 2018

    =   2x

So, a derivative of the inverse is

Note that x = −5 also gives us y = 29, so − is also a derivative. It’s not that hard, once you get the hang

of it.

This is all you’ll be required to know involving derivatives of inverses. Naturally, there are ways to
create harder problems, but the AP Exam stays away from them and sticks to simpler stuff.

Here are some solved problems. Do each problem, cover the answer first, and then check your answer.

PROBLEM 1. Find a derivative of the inverse of f(x) = 2x^3 + 5x + 1 at y = 8.

Answer: First, we take the derivative of f(x).

f′(x)   =   6x^2    +   5

A possible value of x is x = 1.

Then, we use the formula to find the derivative of the inverse.

=

PROBLEM 2. Find a derivative of the inverse of f(x) = 3x^3 − x + 7 at y = 9.

Answer: First, take the derivative of f(x).

f′(x)   =   9x^2    −1

A possible value of x is x = 1.

Then, use the formula to find the derivative of the inverse.

=

PROBLEM 3. Find a derivative of the inverse of at y = at y = 1.