(\partial)/(\partial x)(-210(5x-y)^5)

解

\frac{\partial}{\partial x} (- 210 (5 x - y)^{5})

- 5250 (5 x - y)^{4}

解答ステップ

\frac{\partial}{\partial x} (- 210 (5 x - y)^{5})

y

を定数として扱う

定数を除去:

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

= - 210 \frac{\partial}{\partial x} ((5 x - y)^{5})

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (5 x - y) = 5

= - 210 \cdot 5 (5 x - y)^{4} \cdot 5

簡素化

= - 5250 (5 x - y)^{4}