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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Differentiation

NDA 2019 · Mathematics · Differentiation

Paragraph: Consider the equation x^y=e^ x-y Question: What is (d^2...

Paragraph: Consider the equation xy=ex−yx^y=e^{x-y}
Question: What is d2ydx2\frac{d^2 y}{d x^2} at x=1x=1 equal to?

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

B. 1

Step-by-step solution

∵y1=x−yx(1+ℓnx)⇒y11=x(1+ℓnx)(1−y1)−(x−y)(1+1+ℓnx)x2(1+ℓnx)2⇒y11 at x=1⇒y11=1(1)(1)−01(1)⇒y11=1\begin{aligned} & \because y^1=\frac{x-y}{x(1+\ell \mathrm{n} x)} \\ & \Rightarrow y^{11}=\frac{x(1+\ell \mathrm{n} x)\left(1-y^1\right)-(x-y)(1+1+\ell \mathrm{n} x)}{x^2(1+\ell \mathrm{n} x)^2} \\ & \Rightarrow y^{11} \text{ at } x=1 \\ & \Rightarrow y^{11}=\frac{1(1)(1)-0}{1(1)} \\ & \Rightarrow y^{11}=1\end{aligned}
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