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JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    The derivative of \[{{\cos }^{-1}}\,\left( \frac{{{x}^{-1}}-x}{{{x}^{-1}}+x} \right)\] at \[x=1\] is

    A)  -2                               

    B)  -1             

    C)  0                                

    D)  1

    Correct Answer: D

    Solution :

     Let      \[y={{\cos }^{-1}}\,\left( \frac{{{x}^{-1}}-x}{{{x}^{-1}}+x} \right)\] \[y={{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\] \[y=2\,{{\tan }^{-1}}\,x\] \[\frac{dy}{dx}=\frac{2}{1+{{x}^{2}}}\] At \[x=-1\] \[\frac{dy}{dx}=1\]


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