1. 2016 Derivatives of Inverse Trig Functions
AP Calculus

2. Inverse Trig Functions
sin(y) = x
y = sin-1(x) (with restrictions)
y = sin(x)

3. Inverse Trig Functions with Restrictions

4. Remember : Implicit differentiation

5. Remember: Pythagorean Relationsc a y C b A
a or b unknown
c unknown

6. Inverse Trig: Arcsine 1 x y Chain Rule:
INVERSE dx/dy = 1/(dy/dx) ….. dy/dx = cos(y) … dydx
USE IMPLICIT DIFF!
Chain Rule:

7. EX:
Find the derivative:
Find the derivative.

8. Inverse Trig: Arctangentx y 1
Chain Rule:

9. EX:
Find the derivative:

10. Inverse Trig: Arcsecantx y 1
Chain Rule:

11. Arcsine with the Chain Rule: u = f(x)
Learn these in PAIRS:
Arccosine with the Chain Rule: u = f(x)

12. Arctangent with the Chain Rule: u = f(x)
Learn these in PAIRS:
Arccotangent with the Chain Rule: u = f(x)

13. Inverse Trig: with the Chain Rule: u = f(x)
Learn these in PAIRS:

14. Last Update
10/19/10
Assignment: p 170 # odd , 27-29