Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
- \(\frac{y}{2y + x}\)
-
\(\frac{-y}{2y + x}\)
- \(\frac{-y}{2y - x}\)
- \(\frac{y}{2y + x}\)
The correct answer is: 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 \(\frac{dy}{dx}\)
\(=\frac{dy}{dx}(2y+x)=-y\)
\(∴\frac{dy}{dx}=\frac{-y}{2y + x}\)