Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
FURTHER MATHEMATICS
WAEC 2023
Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
- A. \(\frac{y}{2y + x}\)
- B. \(\frac{-y}{2y + x}\)
- C. \(\frac{-y}{2y - x}\)
- D. \(\frac{y}{2y + x}\)
Correct Answer: B. \(\frac{-y}{2y + x}\)
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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