If $y=e^{x+e^{x+..... to ~\infty}}$, then $\frac{d y}{d x}$ is :
Answer & explanation
Correct answer: option 3
$y=e^{x+y} \Rightarrow \log y=x+y$
$\Rightarrow \frac{1}{y} \frac{d y}{d x}=1+\frac{d y}{d x} \Rightarrow \frac{d y}{d x}=\frac{y}{1-y}$
Hence (3) is correct answer.