derivative 1-(1-0.01x)^3

解

導関数

1 - (1 - 0.01 x)^{3}

0.000003 x^{2} - 0.0006 x + 0.03

解答ステップ

\frac{d}{d x} (1 - (1 - 0.01 x)^{3})

簡素化

1 - (1 - 0.01 x)^{3} : 0.000001 x^{3} - 0.0003 x^{2} + 0.03 x

= \frac{d}{d x} (0.000001 x^{3} - 0.0003 x^{2} + 0.03 x)

和/差の法則を適用:

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

= \frac{d}{d x} (0.000001 x^{3}) - \frac{d}{d x} (0.0003 x^{2}) + \frac{d}{d x} (0.03 x)

\frac{d}{d x} (0.000001 x^{3}) = 0.000003 x^{2}

\frac{d}{d x} (0.0003 x^{2}) = 0.0006 x

\frac{d}{d x} (0.03 x) = 0.03

= 0.000003 x^{2} - 0.0006 x + 0.03