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KCET2022MathematicsDifferentiation

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

Options

  1. A10
  2. B33
  3. C35
  4. D12

Correct answer

B. 33

Step-by-step solution

Let y=f(f(f(x)))+(f(x))^2 Differentiating w.r.t. x , we get aligned & d y d x =f^ (f(f(x))) f^ (f(x)) f^ (x)+2 f(x) f^ (x) & At x=1 & d y d x =f^ (f(f(1))) f^ (f(1)) f^ (1)+2 f(1) f^ (1) & d y d x =f^ (f(1)) f^ (1) 3+2 1 3=f^ (1) 3 3+6 &=9 f^ (1)+6=9 3+6=27+6=33 aligned

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