Q105 / 225 · JEE Main 2004 · Mathematics

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

  • A
    $\frac{\mathrm{x}}{1+\mathrm{x}}$
  • B
    $\frac{1}{x}$
  • Correct answer
    C
    $\frac{1-x}{x}$
  • D
    $\frac{1+x}{x}$

Solution

$x=e^{y+e^{y+e^{y+\ldots \ldots \infty}}} \Rightarrow x=e^{y+x}$ $\Rightarrow \ln x-x=y \Rightarrow \frac{d y}{d x}=\frac{1}{x}-1=\frac{1-x}{x}$

Hence, the correct answer is option: 'C'.

Relevant Questions