Derivative Rule of Inverse Trig Functions

ALL 1 or -1 as numerator & multiplied by du/dx & inverse of u; CO... = -1. sin/cos square root of subtraction. tan/cot adding. csc/sec absolute value * square root switch

$\sin^{-1}x$ range

$$-\frac{\pi}{2}\le y\le\frac{\pi}{2}$$

$\cos^{-1}x$ range

$$0\le y\le\pi$$

$\tan^{-1}x$ range

$$-\frac{\pi}{2}<y<\frac{\pi}{2}$$

$\cot^{-1}x$ range

$$0<y<\pi$$

$\csc^{-1}x$ range

$-\frac{\pi}{2}\le y\le\frac{\pi}{2}$ , $y\ne0$

$\sec^{-1}x$ range

$0\le y\le\pi$ , $y\ne\frac{\pi}{2}$