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