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Question: Answered & Verified by Expert
If $x=e^{y+e^{y+. .10 \infty}}, x>0$, then $\frac{d y}{d x}$ is
MathematicsDifferentiationJEE MainJEE Main 2004
Options:
  • A
    $\frac{\mathrm{x}}{1+\mathrm{x}}$
  • B
    $\frac{1}{x}$
  • C
    $\frac{1-x}{x}$
  • D
    $\frac{1+x}{x}$
Solution:
1710 Upvotes Verified Answer
The correct answer is:
$\frac{1-x}{x}$
$x=e^{y+e^{y+e^{y+\ldots \ldots \infty}}} \Rightarrow x=e^{y+x}$
$\Rightarrow \ln x-x=y \Rightarrow \frac{d y}{d x}=\frac{1}{x}-1=\frac{1-x}{x}$

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