derivative-2x^2(x+4)

解

導関数

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

- 2 (3 x^{2} + 8 x)

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = x + 4

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (x + 4) = 1

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

簡素化

- 2 (2 x (x + 4) + 1 \cdot x^{2}) : - 2 (3 x^{2} + 8 x)

= - 2 (3 x^{2} + 8 x)