d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}})

解

\frac{d}{d y} (\frac{x ln ( \frac{x y}{z} )}{z})

\frac{x}{y z}

解答ステップ

\frac{d}{d y} (\frac{x ln ( \frac{x y}{z} )}{z})

定数を除去:

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

= \frac{x}{z} \frac{d}{d y} (ln (\frac{x y}{z}))

連鎖法則を適用:

\frac{1}{\frac{x y}{z}} \frac{d}{d y} (\frac{x y}{z})

= \frac{1}{\frac{x y}{z}} \frac{d}{d y} (\frac{x y}{z})

\frac{d}{d y} (\frac{x y}{z}) = \frac{x}{z}

= \frac{x}{z} \cdot \frac{1}{\frac{x y}{z}} \cdot \frac{x}{z}

簡素化

\frac{x}{z} \cdot \frac{1}{\frac{x y}{z}} \cdot \frac{x}{z} : \frac{x}{y z}

= \frac{x}{y z}