Derivatives of Trigonometric Inverse Functions

Suppose that you want to find the derivative of
How the hell do we do that?

So we want to find , the derivative of y with respect to x.

Well, the inverse sine is... the inverse of the sine!
In a sense, we can use this in the equivalent expression

Let's differentiate with respect to x, implicitly.

Feels good, huh? Let's practice!
Practice Implicit Differentiation and Derivatives of Trigonometric Inverse Functions - The Inverse Cosine