Correct Answer: Option B

Explanation

\(y^2 + xy = 5\)

By implicit differentiation

\(=2y\frac{dy}{dx}+y+x\frac{dy}{dx}=0\)

\(=2y\frac{dy}{dx}+x\frac{dy}{dx}=-y\)

Factor out \(\frac{dy}{dx}\)

\(=\frac{dy}{dx}(2y+x)=-y\)

\(∴\frac{dy}{dx}=\frac{-y}{2y + x}\)

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