If y² + 2xy - 8 = 0, find \;dy/dx

Correct Answer is : −yy+x\;-y/y+xy+x−y

Correct Answer is : −yy+x\;-y/y+xy+x−y

Test Index

WAEC Further Mathematics 2024 Paper

Question : 31

Total: 40

If y

^{2}

\;\frac{dy}{dx}

Solution:

Concept:

Use implicit differentiation because

y

is a function of

x

Explanation:

Given:

y^2 + 2xy - 8 = 0

Differentiate both sides with respect to

x

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

Group the terms containing

\frac{dy}{dx}

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

Solve for

\frac{dy}{dx}

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

Answer:

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

Therefore, the correct option is A.

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