Given that y² + xy = 5,{ find }dy/dx.

Correct Answer is : −y2y + x\;-y/2y\;+\;x2y+x−y

Correct Answer is : −y2y + x\;-y/2y\;+\;x2y+x−y

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WAEC Further Mathematics 2023 Paper

Question : 32

Total: 40

Given that

y^2 + xy = 5,\text{ find }\frac{dy}{dx}

Solution:

$y^2 + xy = 5$

By implicit differentiation

$=2y\;\frac{dy}{dx}+y+x\;\frac{dy}{dx}=0$

$=2y\;\frac{dy}{dx}+x\;\frac{dy}{dx}=-y$

Factor out $\;\frac{dy}{dx}$

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

$\therefore\;\frac{dy}{dx}=\;\frac{-y}{2y\;+\;x}$

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