Q231 / 270 · NDA 2012 (Phase 1) · Mathematics

If $y=\frac{x+1}{x-1}$, then what is $\frac{d y}{d x}$ equal to?

  • A
    $\frac{-2}{x-1}$
  • Correct answer
    B
    $\frac{-2}{(x-1)^2}$
  • C
    $\frac{2}{(x-1)^2}$
  • D
    $\frac{2}{(x-1)}$

Solution

$\begin{aligned} y & =\frac{x+1}{x-1} \\ \frac{d y}{d x} & =\frac{(x-1)(1)-(x+1) 1}{(x-1)^2} \\ & =\frac{x-1-x-1}{(x-1)^2}=\frac{-2}{(x-1)^2} .\end{aligned}$

Hence, the correct answer is option: 'B'.

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