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AP EAMCET202422 May 2024Morning ShiftMathematicsDifferentiationActual

If f(0)=0, f^ (0)=3 , then the derivative of y=f(f(f(f(f(x))))) at x=0 is

Options

  1. A16
  2. B32
  3. C81
  4. D243

Correct answer

D. 243

Step-by-step solution

aligned & f(0)=0, f^ (0)=3 & y=f(f(f(f(f(x))))) & d y d x =f^ (f(f(f(f(x))))) f^ (f(f(f(x)))) aligned f^ (f(f(x))) f^ (f(x)) f^ (x) array r . d y d x |_ x=0 =f^ (f(f(f(f(0))))) f^ (f(f(f(0)))) f^ (f(f(0))) f^ (f(0)) f^ (0) array = [f^ (0) ]^5=3^5=243 .

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