(\partial)/(\partial x)(4ln((2xy)/(7z)))

解

\frac{\partial}{\partial x} (4 ln (\frac{2 x y}{7 z}))

\frac{4}{x}

解答ステップ

\frac{\partial}{\partial x} (4 ln (\frac{2 x y}{7 z}))

y, z

を定数として扱う

定数を除去:

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

= 4 \frac{\partial}{\partial x} (ln (\frac{2 x y}{7 z}))

連鎖法則を適用:

\frac{1}{\frac{2 x y}{7 z}} \frac{\partial}{\partial x} (\frac{2 x y}{7 z})

= \frac{1}{\frac{2 x y}{7 z}} \frac{\partial}{\partial x} (\frac{2 x y}{7 z})

\frac{\partial}{\partial x} (\frac{2 x y}{7 z}) = \frac{2 y}{7 z}

= 4 \cdot \frac{1}{\frac{2 x y}{7 z}} \cdot \frac{2 y}{7 z}

簡素化

4 \cdot \frac{1}{\frac{2 x y}{7 z}} \cdot \frac{2 y}{7 z} : \frac{4}{x}

= \frac{4}{x}