Question

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

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

Answer 1

The correct option is B

$\frac{1-x}{x}$

x = $e^{y+x}$ $\Rightarrow lo{g}_{e}x$ = y + x

$\therefore \frac{1}{x}$ = $\frac{dy}{dx}+1$

$\Rightarrow \frac{dy}{dx}$ = $\frac{1-x}{x}$