Найдите производную функции f(x) в точке  x0 : [latex]f(x)= \frac{x}{3}- \frac{3}{x} , x _{0}=3. [/latex]

[latex]f(x)= \frac{x}{3} - \frac{3}{x} \\ f'(x)= \frac{1}{3} + \frac{3}{ x^{2} } \\ f'(3)= \frac{1}{3} + \frac{3}{ 3^{2} } = \frac{1}{3} + \frac{1}{3}= \frac{2}{3} [/latex]

[latex]f'(x)=( \frac{x}{3} - \frac{3}{x} )'=( \frac{x}{3})'-( \frac{3}{x} )'= \frac{1}{3} -(- \frac{3}{x^2})= \frac{1}{3} + \frac{3}{x^2} [/latex] [latex]f(3)= \frac{1}{3} + \frac{3}{3^2} = \frac{1}{3} + \frac{3}{9} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}[/latex]