Answer
$\displaystyle \frac{dy}{dx}=\frac{2x}{y}$
Work Step by Step
Differentiating an equation containing
terms of form $f(x)$ and $g(y)$,
terms $f(x)$ are differentiated directly, $\displaystyle \frac{d}{dx}[f(x)],$
and
terms $g(y)$ are differentiated using the chain rule,
$\displaystyle \frac{d}{dx}[g(y)]=\frac{d}{dy}[g(y)]\cdot\frac{dy}{dx}$
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LHS: sum, second term: chain rule
RHS: constant
$2x^{2}-y^{2}=4$
$4x-2y\displaystyle \cdot\frac{dy}{dx}=0\qquad/-4x$
$-2y\displaystyle \cdot\frac{dy}{dx}=-4x\qquad/\div(-2y)$
$\displaystyle \frac{dy}{dx}=\frac{-4x}{-2y}=\frac{2x}{y}$
