derivative of (3x^2+2sqrt(x)/x)

解

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{x})

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

解答ステップ

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

\frac{d}{d x} (3 x^{2} + 2 x) = 6 x + \frac{1}{x}

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

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

簡素化

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

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