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If f(x) and g(x) are two functions with g(x)=x- 1 x and f o g(x)=x³- 1 x³ , then f^ (x)=

Options

  1. A3 x²+ 3 x⁴
  2. B1+ 1 x²
  3. Cx²- 1 x²
  4. D3 x²+3

Correct answer

D. 3 x²+3

Step-by-step solution

f g(x) =x³- 1 x³ aligned f (x- 1 x ) &= (x- 1 x ) (x²+ 1 x² +1 ) &= (x- 1 x ) (x- 1 x )²+2+1 aligned f (x- 1 x )= (x- 1 x ) (x- 1 x )²+3 Replace x- 1 x by xf(x)=(x) (x²+3 )=x³+3 xf^ (x)=3 x²+3

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