derivative 3x^4(2x^2-1)

解

導関数

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

3 (12 x^{5} - 4 x^{3})

解答ステップ

\frac{d}{d x} (3 x^{4} (2 x^{2} - 1))

定数を除去:

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

= 3 \frac{d}{d x} (x^{4} (2 x^{2} - 1))

積の法則を適用:

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

f = x^{4}, g = 2 x^{2} - 1

= 3 (\frac{d}{d x} (x^{4}) (2 x^{2} - 1) + \frac{d}{d x} (2 x^{2} - 1) x^{4})

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

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

= 3 (4 x^{3} (2 x^{2} - 1) + 4 x x^{4})

簡素化

3 (4 x^{3} (2 x^{2} - 1) + 4 x x^{4}) : 3 (12 x^{5} - 4 x^{3})

= 3 (12 x^{5} - 4 x^{3})