Answer: Take the derivative of y.
y′ = −Find the value of x where y = 1.
1 =
x = 2Use the formula.
Here’s one more.
PROBLEM 4. Find a derivative of the inverse of y = 2x − x^3 at y = 1.
Answer: The derivative of the function is
= 2 − 3x^2Next, find the value of x where y = 1. By inspection, y = 1 when x = 1.
Then, we use the formula to find the derivative of the inverse.
PRACTICE PROBLEM SET 15
Find a derivative of the inverse of each of the following functions. The answers are in Chapter 19.
1.y = x + at y = ; where x > 12.y = 3x − 5x^3 at y = 2