derivative 6x(x^2-1)^2

解

導関数

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

6 (5 x^{4} - 6 x^{2} + 1)

解答ステップ

\frac{d}{d x} (6 x (x^{2} - 1)^{2})

定数を除去:

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

= 6 \frac{d}{d x} (x (x^{2} - 1)^{2})

積の法則を適用:

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

f = x, g = (x^{2} - 1)^{2}

= 6 (\frac{d x}{d x} (x^{2} - 1)^{2} + \frac{d}{d x} ((x^{2} - 1)^{2}) x)

\frac{d x}{d x} = 1

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

= 6 (1 \cdot (x^{2} - 1)^{2} + 4 x (x^{2} - 1) x)

簡素化

6 (1 \cdot (x^{2} - 1)^{2} + 4 x (x^{2} - 1) x) : 6 (5 x^{4} - 6 x^{2} + 1)

= 6 (5 x^{4} - 6 x^{2} + 1)