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MHT CET202416 May 2024Morning ShiftMathematicsDifferentiationActual

If f(1)=1, f^ (1)=5 , then the derivative of f ( f ( f (x)))+( f (x))^2 at x=1 is

Options

  1. A125
  2. B1250
  3. C135
  4. D35

Correct answer

C. 135

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) & = f ^ ( f (1)) f ^ (1) 5+2 1 5 & = f ^ (1) 5 5+2 1 5 & =5 5 5+2 1 5 & =135 aligned

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