(\partial)/(\partial y)(ln(x-9y))

解

\frac{\partial}{\partial y} (ln (x - 9 y))

- \frac{9}{x - 9 y}

解答ステップ

\frac{\partial}{\partial y} (ln (x - 9 y))

x

を定数として扱う

連鎖法則を適用:

\frac{1}{x - 9 y} \frac{\partial}{\partial y} (x - 9 y)

= \frac{1}{x - 9 y} \frac{\partial}{\partial y} (x - 9 y)

\frac{\partial}{\partial y} (x - 9 y) = - 9

= \frac{1}{x - 9 y} (- 9)

簡素化

\frac{1}{x - 9 y} (- 9) : - \frac{9}{x - 9 y}

= - \frac{9}{x - 9 y}