Derivative Rules

$$ \frac{d}{dx} \sin(x) = \cos(x) $$ ## $$ \frac{d}{dx} \cos(x) = -\sin(x) $$ ## $$ \frac{d}{dx} \tan(x) = \sec^2(x) $$ ## $$ \frac{d}{dx} \csc(x) = -\csc(x) \cot(x) $$ ## $$ \frac{d}{dx} \sec(x) = \sec(x) \tan(x) $$ ## $$ \frac{d}{dx} \cot(x) = -\csc^2(x) $$

Inverse Trigonometric Derivatives

$$ \frac{d}{dx} \arcsin(x) = \frac{1}{\sqrt{1-x^2}} $$ # $$ \frac{d}{dx} \arccos(x) = -\frac{1}{\sqrt{1-x^2}} $$ # $$ \frac{d}{dx} \arctan(x) = \frac{1}{1+x^2} $$ # $$ \frac{d}{dx} \operatorname{arcsec}(x) = \frac{1}{|x| \sqrt{x^2-1}} $$ # $$ \frac{d}{dx} \operatorname{arccsc}(x) = -\frac{1}{|x| \sqrt{x^2-1}} $$ # $$ \frac{d}{dx} \operatorname{arccot}(x) = -\frac{1}{1+x^2} $$