Derivative of y=\arccos(x)

Derivative of $y=\mathrm{arccos}\left(x\right)$
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sonorous9n
$y=\mathrm{arccos}\left(x\right)$
$\mathrm{cos}\left(y\right)=\mathrm{cos}\left(\mathrm{arccos}\left(x\right)\right)$
$\mathrm{cos}\left(y\right)=x$
Use the Chain Rule
$-\mathrm{sin}\left(y\right)\frac{dy}{dx}=1$
Solve for $\frac{dy}{dx}$
$\frac{dy}{dx}=-\frac{1}{\mathrm{sin}\left(y\right)}$
$\frac{dy}{dx}=-\frac{1}{\mathrm{sin}\left(\mathrm{arccos}\left(x\right)\right)}$
Now, we can simplify
$\mathrm{sin}\left(\mathrm{arccos}\left(x\right)\right)=\mathrm{cos}\left(\mathrm{arcsin}\left(x\right)\right)=\sqrt{1-{x}^{2}}$
$\frac{dy}{dx}=-\frac{1}{\sqrt{1-{x}^{2}}}$