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Question Number 171546 by Kodjo last updated on 17/Jun/22

$$f\left(x\right)=\frac{-ln\mid x\mid }{x}+x-2,g\left(x\right)=-x^2+1-ln\mid x\mid$$ $$$$ Calculate the derivative of f(x) as a function of g(x)\n

Commented bykaivan.ahmadi last updated on 17/Jun/22

$$f\left(x\right)=\frac{-lnx+x^2-2x}{x}=\frac{g\left(x\right)+x^2-1+x^2-2x}{x}$$ $$=\frac{g\left(x\right)-2x-1}{x}=\frac{g\left(x\right)}{x}-2-\frac{1}{x}$$ $$f^{\prime }\left(x\right)=\frac{{xg}^{\prime }\left(x\right)-g\left(x\right)}{x^2}+\frac{1}{x^2}=\frac{{xg}^{\prime }\left(x\right)-g\left(x\right)+1}{x^2}$$

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