derivative of-2(2x^2-4x-1^2)

解

\frac{d}{d x} (- 2 (2 x^{2} - 4 x - 1)^{2})

- 4 (2 x^{2} - 4 x - 1) (4 x - 4)

解答ステップ

\frac{d}{d x} (- 2 (2 x^{2} - 4 x - 1)^{2})

定数を除去:

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

= - 2 \frac{d}{d x} ((2 x^{2} - 4 x - 1)^{2})

連鎖法則を適用:

2 (2 x^{2} - 4 x - 1) \frac{d}{d x} (2 x^{2} - 4 x - 1)

= 2 (2 x^{2} - 4 x - 1) \frac{d}{d x} (2 x^{2} - 4 x - 1)

\frac{d}{d x} (2 x^{2} - 4 x - 1) = 4 x - 4

= - 2 \cdot 2 (2 x^{2} - 4 x - 1) (4 x - 4)

簡素化

= - 4 (2 x^{2} - 4 x - 1) (4 x - 4)