derivative f(x)=2x^6(x^4-2x)

解

導関数

f (x) = 2 x^{6} (x^{4} - 2 x)

2 (10 x^{9} - 14 x^{6})

解答ステップ

\frac{d}{d x} (2 x^{6} (x^{4} - 2 x))

定数を除去:

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

= 2 \frac{d}{d x} (x^{6} (x^{4} - 2 x))

積の法則を適用:

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

f = x^{6}, g = x^{4} - 2 x

= 2 (\frac{d}{d x} (x^{6}) (x^{4} - 2 x) + \frac{d}{d x} (x^{4} - 2 x) x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 2 (6 x^{5} (x^{4} - 2 x) + (4 x^{3} - 2) x^{6})

拡張

6 x^{5} (x^{4} - 2 x) + (4 x^{3} - 2) x^{6} : 10 x^{9} - 14 x^{6}

= 2 (10 x^{9} - 14 x^{6})