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JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Mathematics
Chapter
Differentiation

JEE Main 2004 · Mathematics · Differentiation

If x=e^ y+e^ y+. .10 ∞ , x>0 , then (d y)/(d x) is

If x=ey+ey+..10∞,x>0x=e^{y+e^{y+. .10 \infty}}, x>0, then dydx\frac{d y}{d x} is

Options

  1. Ax1+x\frac{\mathrm{x}}{1+\mathrm{x}}
  2. B1x\frac{1}{x}
  3. C1−xx\frac{1-x}{x}
  4. D1+xx\frac{1+x}{x}

Correct answer

C. 1−xx\frac{1-x}{x}

Step-by-step solution

x=ey+ey+ey+……∞⇒x=ey+xx=e^{y+e^{y+e^{y+\ldots \ldots \infty}}} \Rightarrow x=e^{y+x} ⇒ln⁡x−x=y⇒dydx=1x−1=1−xx\Rightarrow \ln x-x=y \Rightarrow \frac{d y}{d x}=\frac{1}{x}-1=\frac{1-x}{x}
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