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KCET2023MathematicsFunctions

If f(x) and g(x) are two functions with g(x)=x- 1 x and f g(x)=x^3- 1 x^3 , then f^ (x) is equals to

Options

  1. A3 x^2+ 3 x^4
  2. Bx^2- 1 x^2
  3. C1- 1 x^2
  4. D3 x^2+3

Correct answer

D. 3 x^2+3

Step-by-step solution

Here, g(x)=x- 1 x aligned & f g(x)=x^3- 1 x^3 = (x- 1 x )^3+3 x 1 x (x- 1 x ) & f g(x)= (x- 1 x )^3+3 (x- 1 x ) & f(x)=x^3+3 x & f^ (x)=3 x^2+3 aligned

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