(\partial)/(\partial y)((2x-3y)^3)

解

\frac{\partial}{\partial y} ((2 x - 3 y)^{3})

- 9 (2 x - 3 y)^{2}

解答ステップ

\frac{\partial}{\partial y} ((2 x - 3 y)^{3})

x

を定数として扱う

連鎖法則を適用:

3 (2 x - 3 y)^{2} \frac{\partial}{\partial y} (2 x - 3 y)

= 3 (2 x - 3 y)^{2} \frac{\partial}{\partial y} (2 x - 3 y)

\frac{\partial}{\partial y} (2 x - 3 y) = - 3

= 3 (2 x - 3 y)^{2} (- 3)

簡素化

= - 9 (2 x - 3 y)^{2}