derivative of (4x/(9y))

解

\frac{d}{d x} (\frac{4 x}{9 y})

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

解答ステップ

\frac{d}{d x} (\frac{4 x}{9 y})

定数を除去:

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

= \frac{4}{9} \frac{d}{d x} (\frac{x}{y})

商の法則を適用:

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

= \frac{4}{9} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

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

= \frac{4}{9} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

簡素化

\frac{4}{9} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : \frac{4 ( y - x \frac{d y}{d x} )}{9 y ^{2}}

= \frac{4 ( y - x \frac{d y}{d x} )}{9 y ^{2}}