If y = 1+x/1-x, find dy/dx.

Correct Answer is : 2(1−x)2{2}{(1-x)²}(1−x)22

Correct Answer is : 2(1−x)2{2}{(1-x)²}(1−x)22

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WAEC Further Mathematics 2017 Paper

Question : 21

Total: 40

y = \frac{1+x}{1-x}

\frac{dy}{dx}

Solution:

Concept:

Differentiate the given expression using the quotient rule.

Explanation:

Let

u = 1 + x

and

v = 1 - x

Then

u' = 1

and

v' = -1

Using the quotient rule,

\frac{dy}{dx} = \frac{v u' - u v'}{v^2}

Substitute the values:

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

Simplify the numerator:

(1-x) + (1+x) = 2

So,

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

Answer:

\frac{2}{(1-x)^2}

, which is Option A.

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