If $x=e^{y+e^{y+. .10 \infty}}, x0$, then $\frac{d y}{d x}$ is

Question

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

Aicharya · Accepted Answer

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

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