derivative of (5+3x-6sqrt(x)/x)

解

\frac{d}{d x} (\frac{5 + 3 x - 6 x}{x})

\frac{3 x - 5}{x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{5 + 3 x - 6 x}{x})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 5 + 3 x - 6 x ) x - \frac{d x}{d x} ( 5 + 3 x - 6 x )}{x ^{2}}

\frac{d}{d x} (5 + 3 x - 6 x) = - \frac{3}{x} + 3

\frac{d x}{d x} = 1

= \frac{( - \frac{3}{x} + 3 ) x - 1 \cdot ( 5 + 3 x - 6 x )}{x ^{2}}

簡素化

\frac{( - \frac{3}{x} + 3 ) x - 1 \cdot ( 5 + 3 x - 6 x )}{x ^{2}} : \frac{3 x - 5}{x ^{2}}

= \frac{3 x - 5}{x ^{2}}