Derivada de funciones trigonométricas inversas

$$\quad \frac{d}{dx}\arcsin u=\frac{1}{\sqrt{1-u^{2}}}\frac{du}{dx}\\ -\frac{\pi}{2} <\arcsin u<\frac{\pi}{2}$$ (7)

$$\quad \frac{d}{dx}\arccos u=-\frac{1}{\sqrt{1-u^{2}}}\frac{du}{dx}\\ 0<\arccos u<\pi$$ (8)

$$\quad \frac{d}{dx}\arctan u=\frac{1}{1+u^{2}}\frac{du}{dx}\\ -\frac{\pi}{2}<\arctan u <\frac{\pi}{2}$$ (9)

$$\quad \frac{d}{dx}\arccot u=-\frac{1}{1+u^{2}}\frac{du}{dx}\\ 0<\arccot u<\pi$$ (10)

$$\quad \frac{d}{dx}\arcsec u=\frac{\pm 1}{u\sqrt{u^{2}-1}}\frac{d... ...\\ + Si,\, 0<\arcsec u<\frac{\pi}{2},\quad - Si,\,\frac{\pi}{2}<\arcsec u<\pi$$ (11)

$$\quad \frac{d}{dx}\arccsc u=\frac{\mp 1}{u\sqrt{u^{2}-1}}\frac{d... ... + Si, \, 0<\arccsc u<\frac{\pi}{2},\quad - Si, \, \frac{-\pi}{2}<\arccsc u <0$$ (12)