Differentiating Reciprocal and Inverse Trig Functions (Edexcel A-Level Mathematics): Flashcards

$\frac{d}{dx} \csc(x) = -\csc(x) \cot(x)$

$\frac{d}{dx} \sec(x) = \sec(x) \tan(x)$

$\frac{d}{dx} \cot(x) = -\csc^2(x)$

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

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

$\frac{d}{dx} \arctan(x) = \frac{1}{1 + x^2}$

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

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

$\frac{d}{dx} \operatorname{arccsc}(x) = -\frac{1}{|x| \sqrt{x^2 - 1}}$

$\frac{d}{dx}[\csc(x)] = -\csc(x)\cot(x)$