1. Warm-Up: November 3, 2017 Find 𝑑 2 𝑦 𝑑 𝑥 2 of
Where is 𝑑𝑦 𝑑𝑥 undefined?
4 𝑥 2 −9 𝑦 2 =16

2. Homework Questions?

3. Derivatives of Inverse Trigonometric Functions
Section 4.3

4. Derivatives of Inverse Functions
To find an inverse, we switch x and y
(a, f(a))  (f(a), a)
Thm: (𝑓 −1 )′(𝑎)= 1 𝑓 ′ (𝑏) where 𝑓 −1 𝑎 =𝑏

5. Derivatives of Inverse Functions
Function must be one-to-one
If f is differentiable at every point of an interval and df/dx is never zero on the interval, then f has an inverse and f -1 is differentiable at every point.

6. Derivative of arcsin

7. Inverse Trig Derivatives

8. Inverse Trig Derivatives

9. Inverse Trig Derivatives

10. Inverse Trig Function Identities
Calculator Conversion Identities

11. Example – Find y’