(\partial)/(\partial x)((3x+4y)^5)

解

\frac{\partial}{\partial x} ((3 x + 4 y)^{5})

15 (3 x + 4 y)^{4}

解答ステップ

\frac{\partial}{\partial x} ((3 x + 4 y)^{5})

y

を定数として扱う

連鎖法則を適用:

5 (3 x + 4 y)^{4} \frac{\partial}{\partial x} (3 x + 4 y)

= 5 (3 x + 4 y)^{4} \frac{\partial}{\partial x} (3 x + 4 y)

\frac{\partial}{\partial x} (3 x + 4 y) = 3

= 5 (3 x + 4 y)^{4} \cdot 3

簡素化

= 15 (3 x + 4 y)^{4}