Inverse Trigonometric Derivatives
$\displaystyle \frac{d}{dx} \sin^{-1}(x) = \frac{1}{\sqrt{1-x^2}}$
$\displaystyle \frac{d}{dx} \cos^{-1}(x) = \frac{-1}{\sqrt{1-x^2}}$
$\displaystyle \frac{d}{dx} \tan^{-1}(x) = \frac{1}{1+x^2}$
$\displaystyle \frac{d}{dx} \csc^{-1}(x) = \frac{-1}{x\sqrt{x^2-1}}$
$\displaystyle \frac{d}{dx} \sec^{-1}(x) = \frac{1}{x\sqrt{x^2-1}}$
$\displaystyle \frac{d}{dx} \cot^{-1}(x) = \frac{-1}{1+x^2}$
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