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

Test Index

WAEC Further Mathematics 2020 Paper

Question : 9

Total: 39

Differentiate

\frac{x}{x+1}

with respect to x.

Solution:

Concept:

Use the quotient rule for differentiating

\frac{u}{v}

Explanation:

Let

u = x

and

v = x + 1

Then

\frac{du}{dx} = 1

and

\frac{dv}{dx} = 1

Quotient rule:

\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}

Substitute the values:

\frac{d}{dx}\left(\frac{x}{x+1}\right) = \frac{(x+1)(1) - x(1)}{(x+1)^2}

Simplify the numerator:

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

Answer:

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

, which is option D.

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