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JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation by Substitution

  • question_answer
    The derivative of \[{{\sin }^{2}}x\]with respect to \[{{\cos }^{2}}x\] is  [DCE 2002]

    A)            \[{{\tan }^{2}}x\]

    B)            \[\tan x\]

    C)            \[-\tan x\]

    D)            None of these

    Correct Answer: D

    Solution :

               Let \[y={{\sin }^{2}}x\] and \[z={{\cos }^{2}}x\]            Þ  \[\frac{dy}{dx}=\sin 2x\] and \[\frac{dz}{dx}=-\sin 2x\],   \ \[\frac{dy}{dz}=-1\].


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