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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    If \[y={{\sin }^{-1}}\left( \frac{19}{20}x \right)+{{\cos }^{-1}}\left( \frac{19}{20}x \right)\], then \[\frac{dy}{dx}=\]

    A)            0

    B)            1

    C)            ? 1

    D)            None of these

    Correct Answer: A

    Solution :

               \[y={{\sin }^{-1}}\left( \frac{19}{20}x \right)+{{\cos }^{-1}}\left( \frac{19}{20}x \right)=\frac{\pi }{2}\]                    Þ \[\frac{dy}{dx}=0\],  \[\left( \because {{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} \right)\].


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