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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Critical Thinking

  • question_answer
    If \[{{I}_{n}}=\frac{{{d}^{n}}}{d{{x}^{n}}}({{x}^{n}}\log x),\]then \[{{I}_{n}}-n{{I}_{n-1}}=\] [EAMCET 2003]

    A) \[n\]

    B) \[n-1\]

    C) \[n!\]

    D) \[(n-1)!\]

    Correct Answer: D

    Solution :

    • \[{{I}_{n}}=\frac{{{d}^{n-1}}}{d{{x}^{n-1}}}[{{x}^{n-1}}+n{{x}^{n-1}}\log x]\]           
    • \[{{I}_{n}}=(n-1)!+n{{I}_{n-1}}\] Þ \[{{I}_{n}}-n{{I}_{n-1}}=(n-1)!\].


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