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

解答

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

\frac{x}{y z}

求解步骤

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

将常数提出:

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

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

使用连锁律:

\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}

化简

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

= \frac{x}{y z}

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