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JEE Main & Advanced Mathematics Differentiation Question Bank Mock Test - Limits and Derivatives

  • question_answer
    If \[y=a{{e}^{mx}}+b{{e}^{-mx}}\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y\]is equal to

    A) \[{{m}^{2}}(a{{e}^{mx}}-b{{e}^{-mx}})\]

    B) 1

    C) 0                    

    D) none of these

    Correct Answer: C

    Solution :

    [c] \[y=a{{e}^{mx}}+b{{e}^{-mx}}\] \[\therefore \frac{dy}{dx}=am{{e}^{mx}}=mb{{e}^{-mx}}\] Again \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=a{{m}^{2}}{{e}^{mx}}+{{m}^{2}}b{{e}^{-mx}}\] \[={{m}^{2}}(a{{e}^{mx}}+b{{e}^{-mx}})={{m}^{2}}y\] Or \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\]


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