1. 8. Derivatives of Inverse and Inverse Trig Functions

2. Inverse functions
Inverse functions are functions that have x and y points switched
Therefore, at corresponding points, they have reciprocal slopes

3. Derivative of an inverse function
If f(x) is a function and g(x) is its inverse, and f(a)=b and g(b)=a then
b is a y value of the original function and a is the corresponding x value

4. Example 1
If , find f(1), f’(1), f-1(3), and (f-1)’(3)

5. Example 2
If , find (f-1)’(2)

6. Example 3
If m(x) and n(x) are inverses and if m(5) = -9 and m’(5)=-8/11, find n’(-9)

7. Derivatives of inverse trig functions

8. Example 4
Find the equation of the tangent line to the graph of at x = 1.

9. Example 5
Calculate f’(1/2) where f(x) = arcsin(x2)

10. Example 6

11. Example 7
Differentiate then simplify to a single term

12. Example 8
Find the coordinate of any horizontal tangent and find the equation of any horizontal asymptotes of the derivative of