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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Differentiation

NDA 2012 · Mathematics · Differentiation

If y=(x+1)/(x-1) , then what is (d y)/(d x) equal to?

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

Options

  1. A−2x−1\frac{-2}{x-1}
  2. B−2(x−1)2\frac{-2}{(x-1)^2}
  3. C2(x−1)2\frac{2}{(x-1)^2}
  4. D2(x−1)\frac{2}{(x-1)}

Correct answer

B. −2(x−1)2\frac{-2}{(x-1)^2}

Step-by-step solution

y=x+1x−1dydx=(x−1)(1)−(x+1)1(x−1)2=x−1−x−1(x−1)2=−2(x−1)2.\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}
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