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MHT CET202416 May 2024Morning ShiftMathematicsDifferentiationActual

If f(1)=1 , f^ (1)=3 , then the derivative of f ( f ( f (x)))+( f (x))^2 at x=1 is

Options

  1. A12
  2. B15
  3. C9
  4. D33

Correct answer

D. 33

Step-by-step solution

aligned Let y & = f ( f ( f (x)))+( f (x))^2 ~d y ~d x = & f ^ ( f ( f (x))) f ^ ( f (x)) f ^ (x)+2 f (x) f ^ (x) . d y ~d x |_ x=1 & = f ^ ( f ( f (1))) f ^ ( f (1)) f ^ (1)+2 f (1) f ^ (1) & =3 3 3+2 1 3 & =33 aligned

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