derivative of (2y/x)

解

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

\frac{2 ( x \frac{d y}{d x} - y )}{x ^{2}}

解答ステップ

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

定数を除去:

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

= 2 \frac{d}{d x} (\frac{y}{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 y}{d x} x - \frac{d x}{d x} y}{x ^{2}}

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

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

簡素化

2 \cdot \frac{\frac{d y}{d x} x - 1 \cdot y}{x ^{2}} : \frac{2 ( x \frac{d y}{d x} - y )}{x ^{2}}

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