# How do you find the derivative of arccose^x?

Feb 18, 2017

$- {e}^{x} / \left(\sqrt{1 - {e}^{2 x}}\right)$

#### Explanation:

Use the $\textcolor{b l u e}{\text{standard derivative result}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(\arccos x\right) = - \frac{1}{\sqrt{1 - {x}^{2}}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

differentiate using the color(blue)("chain rule"

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(\arccos \left(f \left(x\right)\right)\right) = - \frac{1}{\sqrt{1 - {\left(f \left(x\right)\right)}^{2}}} . f ' \left(x\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow \frac{d}{\mathrm{dx}} \left(\arccos {e}^{x}\right)$

$= - \frac{1}{\sqrt{1 - {\left({e}^{x}\right)}^{2}}} \times \frac{d}{\mathrm{dx}} \left({e}^{x}\right)$

=-e^x/(sqrt(1-e^(2x))