Answer
$\frac{dy}{dx}=\frac{1}{\ln{2}}\frac{2}{x}$
Work Step by Step
$y=\log_{2}{(\frac{x^2}{2})}=\frac{\ln\frac{x^2}{2}}{ln2}$
On differentiating both sides:
$\frac{dy}{dx}=\frac{1}{ln{2}}\frac{d(\ln\frac{x^2}{2})}{dx}$
$\frac{dy}{dx}=\frac{1}{\ln{2}}\frac{1}{\frac{x^2}{2}}\frac{d(\frac{x^2}{2})}
{dx}$
$\frac{dy}{dx}=\frac{1}{\ln{2}}\frac{2}{x}$
