derivative of (9+4x-6sqrt(x)/x)

解

\frac{d}{d x} (\frac{9 + 4 x - 6 x}{x})

\frac{3 x - 9}{x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{9 + 4 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} ( 9 + 4 x - 6 x ) x - \frac{d x}{d x} ( 9 + 4 x - 6 x )}{x ^{2}}

\frac{d}{d x} (9 + 4 x - 6 x) = - \frac{3}{x} + 4

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

= \frac{( - \frac{3}{x} + 4 ) x - 1 \cdot ( 9 + 4 x - 6 x )}{x ^{2}}

簡素化

\frac{( - \frac{3}{x} + 4 ) x - 1 \cdot ( 9 + 4 x - 6 x )}{x ^{2}} : \frac{3 x - 9}{x ^{2}}

= \frac{3 x - 9}{x ^{2}}