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

Test Index

WAEC Further Mathematics 2011 Paper

Question : 14

Total: 40

y^{2} + xy - x = 0

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

Solution:

Concept:

Implicit differentiation is used because

y

is given implicitly as a function of

x

Explanation:

Start with

y^{2} + xy - x = 0

Differentiate every term with respect to

x

The derivative of

y^{2}

2y\frac{dy}{dx}

For

xy

, use the product rule to get

x\frac{dy}{dx} + y

The derivative of

-x

-1

Thus,

2y\frac{dy}{dx} + x\frac{dy}{dx} + y - 1 = 0

Group the

\frac{dy}{dx}

terms:

(x + 2y)\frac{dy}{dx} = 1 - y

Divide both sides by

x + 2y

to obtain

\frac{dy}{dx} = \frac{1 - y}{x + 2y}

Answer:

\frac{dy}{dx} = \frac{1 - y}{x + 2y}

, so the correct option is C.

Go to Question:

Prev Question

Next Question