(\partial)/(\partial y)((2x+3y)^7)

解

\frac{\partial}{\partial y} ((2 x + 3 y)^{7})

21 (2 x + 3 y)^{6}

解答ステップ

\frac{\partial}{\partial y} ((2 x + 3 y)^{7})

x

を定数として扱う

連鎖法則を適用:

7 (2 x + 3 y)^{6} \frac{\partial}{\partial y} (2 x + 3 y)

= 7 (2 x + 3 y)^{6} \frac{\partial}{\partial y} (2 x + 3 y)

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

= 7 (2 x + 3 y)^{6} \cdot 3

簡素化

= 21 (2 x + 3 y)^{6}