(\partial)/(\partial x)(ln(2x-y))

解

\frac{\partial}{\partial x} (ln (2 x - y))

\frac{2}{2 x - y}

解答ステップ

\frac{\partial}{\partial x} (ln (2 x - y))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 x - y} \frac{\partial}{\partial x} (2 x - y)

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

\frac{\partial}{\partial x} (2 x - y) = 2

= \frac{1}{2 x - y} \cdot 2

簡素化

\frac{1}{2 x - y} \cdot 2 : \frac{2}{2 x - y}

= \frac{2}{2 x - y}