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

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Derivatives of Inverse Trigonometric Functions Section 4.3

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

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.

Derivative of arcsin

Inverse Trig Derivatives

Inverse Trig Derivatives

Inverse Trig Derivatives

Inverse Trig Function Identities Calculator Conversion Identities

Example – Find y’