(\partial)/(\partial x)(2ln(xz))

解

\frac{\partial}{\partial x} (2 ln (x z))

\frac{2}{x}

解答ステップ

\frac{\partial}{\partial x} (2 ln (x z))

z

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

\frac{1}{x z} \frac{\partial}{\partial x} (x z)

= \frac{1}{x z} \frac{\partial}{\partial x} (x z)

\frac{\partial}{\partial x} (x z) = z

= 2 \cdot \frac{1}{x z} z

簡素化

2 \cdot \frac{1}{x z} z : \frac{2}{x}

= \frac{2}{x}