อนุพันธ์ tan

$$ \frac{d}{dx} \tan x = \sec^2 x \\ $$
พิสูจน์

\begin{align} \cssId{Step1}{ \frac{d}{dx} \tan x = \frac{d}{dx} \frac{\sin x}{\cos x} } \\ \cssId{Step2}{ = \frac{\cos x \frac{d}{dx} \sin x - \sin x \frac{d}{dx} \cos x }{\cos^2 x} } \\ \cssId{Step3}{ = \frac{\cos x \cos x - \sin x (-\sin x)}{\cos^2 x} } \\ \cssId{Step4}{ = \frac{\cos^2 x + \sin^2 x }{\cos^2 x} } \\ \cssId{Step5}{ = \frac{1 }{\cos^2 x} } \\ \cssId{Step6}{ = \sec ^2 x } \\ \end{align}