Question

f(x) = (3x + 2)/(5x)

Answer 1

Ответ:

$f(x) = \frac{(3x + 2)}{(5x)}$

$f(x) = \frac{3x + 2}{5x}$

$f'(x) = \frac{d}{dx} ( \frac{3x + 2}{5x} )$

$f'(x) = \frac{d}{dx} ( \frac{3x}{5x} + \frac{2}{5x} )$

сокращаем на общий делитель x:

$f'(x) = \frac{d}{dx} ( \frac{3}{5} + \frac{2}{5x} )$

$f'(x) = \frac{d}{dx} ( \frac{3}{5} ) + \frac{d}{dx} ( \frac{2}{5x} )$

$f'(x) = 0 - 2 \times \frac{ \frac{d}{dx}(5x) }{ {(5x)}^{2} }$

$f'(x) = 0 - 2 \times \frac{5}{ {(5x)}^{2} }$

$f'(x) = - 2 \times \frac{5}{25 {x}^{2} }$

сокращаем на общий делитель 5:

$f'(x) = - 2 \times \frac{1}{5 {x}^{2} }$

$f'(x) = - \frac{2}{5 {x}^{2} }$