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MHT CET202415 May 2024Evening 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. B30
  3. C15
  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) aligned aligned . 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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