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

  • question_answer
    \[\frac{d}{dx}[{{e}^{ax}}\cos (bx+c)]\]=                                                               [AISSE 1989]

    A)            \[{{e}^{ax}}[a\cos (bx+c)-b\sin (bx+c)]\]

    B)            \[{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]\]

    C)            \[{{e}^{ax}}[\cos (bx+c)-\sin (bx+c)]\]

    D)            None of these

    Correct Answer: A

    Solution :

               \[\frac{d}{dx}[{{e}^{ax}}\cos (bx+c)]\]=\[\frac{dx}{dt}=-2\sin t+2\sin 2t\]                                                                   =\[{{e}^{ax}}[a\cos (bx+c)-b\sin (bx+c)]\].


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