| Derivative Function | Domain of the Derivative Function |
|---|---|
| \(\dfrac{d}{dx}\sin x=\cos x\) | \(( -\infty ,\infty ) \) |
| \(\dfrac{d}{dx}\cos x=-\sin x\) | \(( -\infty ,\infty ) \) |
| \(\dfrac{d}{dx}\tan x=\sec ^{2}x\) | \(\left\{ x|x\neq \dfrac{2k+1}{2}\pi, k\hbox{ an integer}\right\} \) |
| \(\dfrac{d}{dx}\cot x=-\csc ^{2}x\) | \(\{ x|x\neq k\pi, k \hbox{ an integer}\} \) |
| \(\dfrac{d}{dx}\csc x=-\csc x\cot x\) | \(\{ x|x\neq k\pi, k\hbox{ an integer}\} \) |
| \(\dfrac{d}{dx}\sec x=\sec x\tan x\) | \(\left\{ x|x\neq \dfrac{2k+1}{2}\pi, k\hbox{ an integer}\right\} \) |