(\partial)/(\partial x)((7x+3y)^5)

解

\frac{\partial}{\partial x} ((7 x + 3 y)^{5})

35 (7 x + 3 y)^{4}

解答ステップ

\frac{\partial}{\partial x} ((7 x + 3 y)^{5})

y

を定数として扱う

連鎖法則を適用:

5 (7 x + 3 y)^{4} \frac{\partial}{\partial x} (7 x + 3 y)

= 5 (7 x + 3 y)^{4} \frac{\partial}{\partial x} (7 x + 3 y)

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

= 5 (7 x + 3 y)^{4} \cdot 7

簡素化

= 35 (7 x + 3 y)^{4}