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

Question

Professor PC Thomas Classes · Answer

$x = e^{y+x} \Rightarrow \ln x = y + x \Rightarrow y = \ln x - x \Rightarrow dy/dx = 1/x - 1 = \frac{1-x}{x}$.