What is the derivative of (x + 1)/(x - 1)?

Derivatives & Second-Order Derivatives · Question 8 of 96

Question 8

MediumOriginal question

What is the derivative of $\frac{x + 1}{x - 1}$ ?

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

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

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1

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

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CorrectNot quiteAnswer A

Correct answer: A

Quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$ , with $u = x + 1$ and $v = x - 1$ .
This simplifies to $- \frac{2}{\left(x - 1\right)^{2}}$ .

Worth noting

$\frac{2}{\left(x - 1\right)^{2}}$ has the numerator the wrong way round: it is $u'v - uv'$ , not $uv' - u'v$ .

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.