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

Test Index

WAEC Further Mathematics 2023 Paper

Question : 32

Total: 40

Given that

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

Solution:

Concept:

Use implicit differentiation on both sides of the equation with respect to

x

Explanation:

Differentiate each term of

y^2 + xy = 5

\frac{d}{dx}(y^2) + \frac{d}{dx}(xy) = \frac{d}{dx}(5)

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

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

Factor out

\frac{dy}{dx}

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

Divide both sides by

(2y + x)

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

Answer:

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

, which is option B.

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