Ch. 4 – More Derivatives 4.3 – Derivatives of Inverse Trig Functions

Ex: Differentiate y = sin -1 x. –Rewrite it without inverse trig functions, then do implicit differentiation… –To evaluate sec(sin -1 x), let’s examine a right triangle with sinθ=x: –Using Pythagorean Thm., we find that the 3 rd side of the triangle is… –The secant of our angle θ then would be… x 1 θ

Using similar logic, we determine the following derivatives of inverse trig functions: To find the derivatives of the other 3 inverse trig functions: Memorize these !

Ex: Differentiate y = tan -1 (4x). Ex: Differentiate y = 2xcos -1 (x).

Ex: Differentiate y = sin -1 (x 2 – 1).