JEE Main & Advanced AIEEE Solved Paper-2004

  • 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   

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