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NDA2024MathematicsDifferentiationActual

Let f(x) and g(x) be two functions such that g(x)=x- 1 x and f o g(x)=x^3- 1 x^3 . What is f^ (x) equal to?

Options

  1. A- 2 x^3
  2. B2 x+ 2 x^3
  3. C6 x+3
  4. D6 x

Correct answer

D. 6 x

Step-by-step solution

f(x) and g(x) are two functions aligned g(x) & =x- 1 x and f o g(x)=x^3- 1 x^3 f (x- 1 x ) & =x^3- 1 x^3 f (x- 1 x ) & = (x- 1 x )^3+3 (x- 1 x ) aligned aligned f^ (x) & =3 x^2+3 f^ (x) & =6 x aligned

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