# derivative of cos^(-1)x

derivative of ${\mathrm{cos}}^{-1}x$
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Emaidedip6g
Let ${\mathrm{cos}}^{-1}x$
$⇒x=\mathrm{cos}y$
differentiate it with respect to y, we get
$\frac{dx}{dy}=-\mathrm{sin}y$
$⇒{\mathrm{sin}}^{2}y=1-{\mathrm{cos}}^{2}y$
$⇒{\mathrm{sin}}^{2}y=1-{x}^{2}$
$⇒\mathrm{sin}y=\sqrt{1-{x}^{2}}$
$⇒\frac{dx}{dy}=-\sqrt{1-{x}^{2}}$
$⇒\frac{dx}{dy}=\frac{1}{\frac{dx}{dy}}=-\frac{1}{\sqrt{1-{x}^{2}}}$