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JEE Main & Advanced AIEEE Solved Paper-2013

  • question_answer
    If\[y=sec(ta{{n}^{-1}}x),\]then\[\frac{dy}{dx}\]at\[x=1\]is equal to:     AIEEE Solevd Paper-2013

    A) \[\frac{1}{\sqrt{2}}\]                     

    B)        \[\frac{1}{2}\]                   

    C)        1                             

    D)        \[\sqrt{2}\]

    Correct Answer: A

    Solution :

    \[y=sec(ta{{n}^{-1}}x)\] \[\Rightarrow \] \[\frac{dy}{dx}=sec(ta{{n}^{-1}}x)\cdot tan(ta{{n}^{-1}}x).\frac{1}{1+{{x}^{2}}}\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{x=1}}=\frac{\sqrt{2}}{1+1}=\frac{1}{\sqrt{2}}\]


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