derivative y=2x^2(3x-4)

解

導関数

y = 2 x^{2} (3 x - 4)

2 (9 x^{2} - 8 x)

解答ステップ

\frac{d}{d x} (2 x^{2} (3 x - 4))

定数を除去:

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

= 2 \frac{d}{d x} (x^{2} (3 x - 4))

積の法則を適用:

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

f = x^{2}, g = 3 x - 4

= 2 (\frac{d}{d x} (x^{2}) (3 x - 4) + \frac{d}{d x} (3 x - 4) x^{2})

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

\frac{d}{d x} (3 x - 4) = 3

= 2 (2 x (3 x - 4) + 3 x^{2})

拡張

2 x (3 x - 4) + 3 x^{2} : 9 x^{2} - 8 x

= 2 (9 x^{2} - 8 x)