A) \[\frac{1+x}{x}\]
B) \[\frac{1}{x}\]
C) \[\frac{1-x}{x}\]
D) \[\frac{x}{1+x}\]
Correct Answer: C
Solution :
\[x={{e}^{y+{{e}^{y+....to\,\infty }}}}\], \[x>0\], \[x={{e}^{y+x}}\] Taking log to the both sides, \[\log x=(y+x)\] Differentiate both sides w.r.t. x, \[\frac{1}{x}=\frac{dy}{dx}+1\] \[\Rightarrow \frac{dy}{dx}=\frac{1-x}{x}\].
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