derivative f(x)=(2sqrt(x))/x

解

導関数

f (x) = \frac{2 x}{x}

- \frac{1}{x ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d x} (\frac{2 x}{x})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{x})

商の法則を適用:

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

= 2 \cdot \frac{\frac{d}{d x} ( x ) x - \frac{d x}{d x} x}{x ^{2}}

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= 2 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

簡素化

2 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{1}{x ^{\frac{3}{2}}}

= - \frac{1}{x ^{\frac{3}{2}}}