Differentiate x/x+1 with respect to x.

Correct Answer is : 1(x+1)21/(x+1)²(x+1)21

Correct Answer is : 1(x+1)21/(x+1)²(x+1)21

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WAEC Further Mathematics 2012 Paper

Question : 20

Total: 40

Differentiate

\frac{x}{x+1}

with respect to x.

Solution:

Concept:

The function is a quotient of two differentiable functions, so apply the quotient rule.

Explanation:

Let

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

Take

u = x

and

v = x+1

Then

\frac{du}{dx} = 1

and

\frac{dv}{dx} = 1

Using the quotient rule,

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

Substitute the values:

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

Simplify the numerator:

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

Therefore,

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

Answer:

The correct option is B:

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

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