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

  • question_answer
    \[\frac{d}{dx}\left[ \frac{{{e}^{ax}}}{\sin (bx+c)} \right]=\]                                   [AI CBSE 1983]

    A)            \[\frac{{{e}^{ax}}[a\sin (bx+c)+b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\]

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

    C)            \[\frac{{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\]

    D)            None of these

    Correct Answer: C

    Solution :

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


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