1. Find the derivative Find the second derivative
Warm-up
Find the derivative
Find the second derivative

2. 16. Section 3.9 Derivatives of Inverse Functions

3. Derivatives of Inverse Functions
EQ – How do you find the derivative of an inverse function?

4. Derivative of an inverse function
If f(x) is a function and g(x) is its inverse,
Steps
Find the inverse (g(x))
Find f’(x)
Plug inverse in for x in f’(x)

5. Example
Find g’(x) if f(x) = x2 + 4

6. Derivatives of Inverse Trig Functions
Using the method we used before, we can come up with equations for derivatives of inverse trig functions

7. Example Calculate f’(1/2) where f(x) = arcsin(x2)
(remember arcsin is another notation for sin-1)
(You need to use chain rule)

8. The rest of inverse trig functions

9. Example
Calculate f’(x) where f(x) = tan-1(3x+1)

10. Example
Find when x = 0

11. Assignment
Pg. 191: #1-7 odd, odd