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

解

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

\frac{2}{x + 2 y}

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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