A Summary

Inverse Trigonometric Derivatives

Learn these:

$\displaystyle \frac{d}{dx} \sin^{-1}(x) = \frac{1}{\sqrt{1-x^2}}$

$\displaystyle \frac{d}{dx} \tan^{-1}(x) = \frac{1}{1+x^2}$

Ask your instructor if you also need to learn this:

$\displaystyle \frac{d}{dx} \sec^{-1}(x) = \frac{1}{x\sqrt{x^2-1}}$

We do not expect you to learn these:

$\displaystyle \frac{d}{dx} \cos^{-1}(x) = \frac{-1}{\sqrt{1-x^2}}$

$\displaystyle \frac{d}{dx} \csc^{-1}(x) = \frac{-1}{x\sqrt{x^2-1}}$

$\displaystyle \frac{d}{dx} \cot^{-1}(x) = \frac{-1}{1+x^2}$