Derivatives of Inverse Trig Functions

3.6

$$\frac{d}{dx}\left\lbrack\mathrm{arcsin}\left(\frac{u}{a}\right)\right\rbrack=$$

$$\frac{u^{\prime}}{\sqrt{a^2-u^2}}$$

\frac{d}{\differentialD x}\left\lbrack\text{arccos}\left(\frac{u}{a}\right)\right\rbrack=

$$\frac{-u^{\prime}}{\sqrt{a^2-u^2}}$$

$$\frac{d}{dx}\arctan\left\lbrack\left(\frac{u}{a}\right)\right\rbrack=$$

$$\frac{a^{}}{a^2+u^2}$$

$$\frac{d}{dx}\left\lbrack arc\cot\left(\frac{u}{a}\right)\right\rbrack=$$

$$\frac{-u^{\prime}}{a^2-u^2}$$

$$\frac{d}{dx}\left\lbrack\operatorname{arcsec}\left(u\right)\right\rbrack=$$

$$\frac{u^{\prime}}{\left|u\right|\sqrt{u^{^2}-1}}$$

$$\frac{d}{dx}\left\lbrack\operatorname{arccsc}\left(u\right)\right\rbrack=$$

$$\frac{-u^{\prime}}{\left|u\right|\sqrt{u^2-1}}$$