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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Differentiation

NDA 2022 · Mathematics · Differentiation

In y= ^2 ((x^2-x+1)/(x^2+x+1)), then what is (d y)/(d x) at x=0...

In y=ln⁡2(x2−x+1x2+x+1),thenwhatisdydxaty=\ln ^2 \left(\frac{x^2-x+1}{x^2+x+1}\right), then what is \frac{d y}{d x} at x=0equalto?equal to?

Options

  1. A−2-2
  2. B00
  3. C11
  4. D22

Correct answer

B. 00

Step-by-step solution

y=[ln⁡(x2−x+1x2+x+1)]2dydx=2ln⁡(x2−x+1x2+x+1)×x2+x+1x2−x+1×(2x−1)(x2+x+1)−(2x+1)(x2−x+1)(x2+x−1)2\begin{aligned} y= & {\left[\ln \left(\frac{x^2-x+1}{x^2+x+1}\right)\right]^2 } \\ \frac{d y}{d x}= & 2 \ln \left(\frac{x^2-x+1}{x^2+x+1}\right) \times \frac{x^2+x+1}{x^2-x+1} \\ & \times \frac{(2 x-1)\left(x^2+x+1\right)-(2 x+1)\left(x^2-x+1\right)}{\left(x^2+x-1\right)^2}\end{aligned} Put x=0dydx=0\begin{aligned} & \text{ Put } x=0 \\ & \frac{d y}{d x}=0\end{aligned}$
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