(\partial)/(\partial x)(-7(x+2y)^5)

解

\frac{\partial}{\partial x} (- 7 (x + 2 y)^{5})

- 35 (x + 2 y)^{4}

解答ステップ

\frac{\partial}{\partial x} (- 7 (x + 2 y)^{5})

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - 7 \frac{\partial}{\partial x} ((x + 2 y)^{5})

連鎖法則を適用:

5 (x + 2 y)^{4} \frac{\partial}{\partial x} (x + 2 y)

= 5 (x + 2 y)^{4} \frac{\partial}{\partial x} (x + 2 y)

\frac{\partial}{\partial x} (x + 2 y) = 1

= - 7 \cdot 5 (x + 2 y)^{4} \cdot 1

簡素化

= - 35 (x + 2 y)^{4}