Ответ:

[tex]f(x) = \frac{(3x + 2)}{(5x)} [/tex]

[tex]f(x) = \frac{3x + 2}{5x} [/tex]

[tex]f'(x) = \frac{d}{dx} ( \frac{3x + 2}{5x} )[/tex]

[tex]f'(x) = \frac{d}{dx} ( \frac{3x}{5x} + \frac{2}{5x} )[/tex]

сокращаем на общий делитель x:

[tex]f'(x) = \frac{d}{dx} ( \frac{3}{5} + \frac{2}{5x} )[/tex]

[tex]f'(x) = \frac{d}{dx} ( \frac{3}{5} ) + \frac{d}{dx} ( \frac{2}{5x} )[/tex]

[tex]f'(x) = 0 - 2 \times \frac{ \frac{d}{dx}(5x) }{ {(5x)}^{2} } [/tex]

[tex]f'(x) = 0 - 2 \times \frac{5}{ {(5x)}^{2} } [/tex]

[tex]f'(x) = - 2 \times \frac{5}{25 {x}^{2} } [/tex]

сокращаем на общий делитель 5:

[tex]f'(x) = - 2 \times \frac{1}{5 {x}^{2} } [/tex]

[tex]f'(x) = - \frac{2}{5 {x}^{2} } [/tex]