Topic: Mathematics
If $x=e^{y+e^{y+e^{y+e^{y+...}}}}$ then $\frac{dy}{dx}$ is
- A. $(1-x)$
- B. $(1-x)/x$
- C. $1/x$
- D. $x/(1-x)$
Answer: B. $(1-x)/x$
Explanation: $x=e^{y+e^{y+e^{y+...}}}$ It can also be written as $x=e^{y+x}$. Taking log of both sides $log x = y+x$. Differentiating both sides $\frac{1}{x}=\frac{dy}{dx}+1 \Rightarrow \frac{dy}{dx}=\frac{1-x}{x}$.