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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    If \[f(0)=0,f'(0)=2\], then the derivative of \[y=f(f(f(f(x)))\] at \[x=0\] is

    A) 2

    B) 8

    C) 16

    D) 4

    Correct Answer: C

    Solution :

    [c] \[y'(x)=f'(f(f(f(x))))f'(f(f(x)))f'(f(x))f'(x)\] \[\Rightarrow y'(0)=f'(f(f(f(0)))f'(f(f(0)))f'(f(0))f'(0)\] \[=f'(f(f(0)))f'(f(0)))f'(0)f'(0)\] \[=f'(f(0))f'(0)f'(0)f'(0)\] \[=f'(0)f'(0)f'(0)f'(0)={{(f'(0))}^{4}}={{2}^{4}}=16\].


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