derivative of 1000(1-x/(500)^2)

解

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

- 4 (1 - \frac{x}{500})

解答ステップ

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

定数を除去:

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

= 1000 \frac{d}{d x} ((1 - \frac{x}{500})^{2})

連鎖法則を適用:

2 (1 - \frac{x}{500}) \frac{d}{d x} (1 - \frac{x}{500})

= 2 (1 - \frac{x}{500}) \frac{d}{d x} (1 - \frac{x}{500})

\frac{d}{d x} (1 - \frac{x}{500}) = - \frac{1}{500}

= 1000 \cdot 2 (1 - \frac{x}{500}) (- \frac{1}{500})

簡素化

1000 \cdot 2 (1 - \frac{x}{500}) (- \frac{1}{500}) : - 4 (1 - \frac{x}{500})

= - 4 (1 - \frac{x}{500})