question_answer

If\[x={{e}^{y+{{e}^{y+....\infty }}}},x>0,\]then\[\frac{dy}{dx}\]is

A) \[\frac{x}{1+x}\]

B)                        \[\frac{1}{x}\]                                   

C) \[\frac{1-x}{x}\]               

D)        \[\frac{1+x}{x}\]

Correct Answer: C

Solution :

Firstly, take log both sides and then differentiation w.r.t..             Taking log on both sides, we get On differentiating w.r.t.we get