(\partial)/(\partial y)((2x+3y)^{10})

解

\frac{\partial}{\partial y} ((2 x + 3 y)^{10})

30 (2 x + 3 y)^{9}

解答ステップ

\frac{\partial}{\partial y} ((2 x + 3 y)^{10})

x

を定数として扱う

連鎖法則を適用:

10 (2 x + 3 y)^{9} \frac{\partial}{\partial y} (2 x + 3 y)

= 10 (2 x + 3 y)^{9} \frac{\partial}{\partial y} (2 x + 3 y)

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

= 10 (2 x + 3 y)^{9} \cdot 3

簡素化

= 30 (2 x + 3 y)^{9}