If y² + xy - x = 0, find \;\;d\;y/\;d\;x.

Correct Answer is : 1 − yx + 2y\;1\;-\;y/x\;+\;2yx+2y1−y

Correct Answer is : 1 − yx + 2y\;1\;-\;y/x\;+\;2yx+2y1−y

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WAEC Further Mathematics 2011 Paper

Question : 14

Total: 40

y^{2} + xy - x = 0

\;\frac{\;d\;y}{\;d\;x}

Solution:

Given $y^{2} + xy - x = 0$

Using the method of implicit differentiation, we have

$2y\;\frac{\;d\;y}{\;d\;x} + x\;\frac{\;d\;y}{\;d\;x} + y - 1 = 0$

$\;\frac{\;d\;y}{\;d\;x}(2y + x) = 1 - y$

$\;\frac{\;d\;y}{\;d\;x} = \;\frac{1\;-\;y}{x\;+\;2y}$

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