If 2y² + 7 = 3y - xy, find \; dy/dx

Correct Answer is : −y4x+x−3\; -y/4x+x-34x+x−3−y

Correct Answer is : −y4x+x−3\; -y/4x+x-34x+x−3−y

Test Index

WAEC Further Mathematics 2021 Paper

Question : 17

Total: 38

If 2y

^{2}

\; \frac{dy}{dx}

Solution:

Concept:

Use implicit differentiation because

y

is a function of

x

Explanation:

Differentiate both sides of

2y^{2}+7=3y-xy

with respect to

x

4y\frac{dy}{dx}=3\frac{dy}{dx}-\left(x\frac{dy}{dx}+y\right)

Simplify the right side:

4y\frac{dy}{dx}=3\frac{dy}{dx}-x\frac{dy}{dx}-y

Collect all

\frac{dy}{dx}

terms:

(4y+x-3)\frac{dy}{dx}=-y

Therefore:

\frac{dy}{dx}=\frac{-y}{4y+x-3}

Answer:

\frac{dy}{dx}=-\frac{y}{4y+x-3}

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