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

解

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

- 20 x^{3} + 36 x^{2} - 18 x + 2

解答ステップ

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

簡素化

2 x (1 - x)^{3} - 3 x^{2} (1 - x)^{2} : - 5 x^{4} + 12 x^{3} - 9 x^{2} + 2 x

= \frac{d}{d x} (- 5 x^{4} + 12 x^{3} - 9 x^{2} + 2 x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (5 x^{4}) + \frac{d}{d x} (12 x^{3}) - \frac{d}{d x} (9 x^{2}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

\frac{d}{d x} (12 x^{3}) = 36 x^{2}

\frac{d}{d x} (9 x^{2}) = 18 x

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

= - 20 x^{3} + 36 x^{2} - 18 x + 2