f-x-ln-x-x-x-2-g-x-x-2-1-ln-x-Calculate-the-derivative-of-f-x-as-a-function-of-g-x-

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

f (x) = \frac{- l n ∣ x ∣}{x} + x - 2, g (x) = - x^{2} + 1 - l n ∣ x ∣

Calculate the derivative of f(x) as a function of g(x)

Commented by kaivan.ahmadi last updated on 17/Jun/22

f (x) = \frac{- l n x + x^{2} - 2 x}{x} = \frac{g (x) + x^{2} - 1 + x^{2} - 2 x}{x}

= \frac{g (x) - 2 x - 1}{x} = \frac{g (x)}{x} - 2 - \frac{1}{x}

f^{'} (x) = \frac{{x g}^{'} (x) - g (x)}{x^{2}} + \frac{1}{x^{2}} = \frac{{x g}^{'} (x) - g (x) + 1}{x^{2}}