Question

If $x=e^{y+e^y+e^{y+...\infty }}$ ,then $\frac{dy}{dx}$ is

• A. $\frac{1}{x}$
• B. $\frac{1-x}{x}$
• C. $\frac{x}{1+x}$
• D. $Noneofthese$

Answer 1

The correct option is B $\frac{1-x}{x}$

$x=e^{y+x}\Rightarrow lo{g}_{e}x=y+x\therefore \frac{1}{x}=\frac{dy}{dx}+1\Rightarrow \frac{dy}{dx}=\frac{1-x}{x}$