Differentiate x² + xy - 5 = 0.

Correct Answer is : −(2x+y)x-(2x + y)/xx−(2x+y)

Correct Answer is : −(2x+y)x-(2x + y)/xx−(2x+y)

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WAEC Further Mathematics 2013 Paper

Question : 11

Total: 40

Differentiate

x^{2} + xy - 5 = 0

Solution:

Concept:

Differentiate implicitly with respect to

x

, treating

y

as a function of

x

Explanation:

Differentiate each term of

x^{2} + xy - 5 = 0

with respect to

x

\frac{d}{dx}(x^{2}) = 2x

Using the product rule,

\frac{d}{dx}(xy) = x\frac{dy}{dx} + y

\frac{d}{dx}(-5) = 0

So,

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

Rearrange to isolate

\frac{dy}{dx}

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

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

Answer:

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

, which is Option A.

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