derivative of x(1-2x^3)

解

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

(1 - 2 x)^{3} - 6 x (1 - 2 x)^{2}

解答ステップ

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

積の法則を適用:

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

f = x, g = (1 - 2 x)^{3}

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

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

\frac{d}{d x} ((1 - 2 x)^{3}) = - 6 (1 - 2 x)^{2}

= 1 \cdot (1 - 2 x)^{3} + (- 6 (1 - 2 x)^{2}) x

簡素化

= (1 - 2 x)^{3} - 6 x (1 - 2 x)^{2}