Identități folosite:
[tex](f \pm g)' = f'\pm g'[/tex]
[tex](x^n)' = nx^{n-1},\quad n-\text{ constant\u{a}}[/tex]
[tex]\left[a\cdot u(x)\right]' = a\cdot u'(x),\quad a - \text{constant\u{a}}[/tex]
[tex](\ln x)' = \frac{1}{x}[/tex]
Rezolvare:
[tex]f(x) = x^2-2\ln x[/tex]
[tex]f'(x) = (x^2-2\ln x)' = (x^2)' - (2\ln x)'=[/tex]
[tex]=(x^2)' - 2\cdot (\ln x)' = 2x^{2-1}-2\cdot \frac{1}{x} =[/tex]
[tex]=2x-\frac{2}{x} =2(x-\frac{1}{x}) = \frac{2(x^2-1)}{x}=[/tex]
[tex]=\frac{2(x-1)(x+1)}{x}[/tex]
