2016 Derivatives of Inverse Trig Functions AP Calculus

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

Inverse Trig Functions with Restrictions

Remember : Implicit differentiation

Remember: Pythagorean Relations c a y C b A a or b unknown c unknown

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

EX: Find the derivative: Find the derivative.

Inverse Trig: Arctangent x y 1 Chain Rule:

EX: Find the derivative:

Inverse Trig: Arcsecant x y 1 Chain Rule:

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

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

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

Last Update 10/19/10 Assignment: p 170 # 1- 21 odd , 27-29