2. Solved Papers
  3. JAMIA MILLIA ISLAMIA

JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

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

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

    B)  \[\frac{1}{x}\]

    C)  \[\frac{1-x}{x}\]

    D)  \[\frac{1+x}{x}\]

    Correct Answer: C

    Solution :

                    \[x={{e}^{y+{{e}^{y+.....\infty }}}}\] \[\therefore \]\[x={{e}^{y+x}}\] Taking log on both sides, we get                 \[\log x=(y+x)\] Differentiate w.r. to\[x,\]we get                 \[\frac{1}{x}=\frac{dy}{dx}+1\Rightarrow \frac{dy}{dx}=\frac{1-x}{x}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner