derivative 500x-0.003x^2+10^{-8}x^3

解

導関数

500 x - 0.003 x^{2} + 1 0^{- 8} x^{3}

500 - 0.006 x + 0.00000003 x^{2}

解答ステップ

\frac{d}{d x} (500 x - 0.003 x^{2} + 1 0^{- 8} x^{3})

和/差の法則を適用:

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

= \frac{d}{d x} (500 x) - \frac{d}{d x} (0.003 x^{2}) + \frac{d}{d x} (1 0^{- 8} x^{3})

\frac{d}{d x} (500 x) = 500

\frac{d}{d x} (0.003 x^{2}) = 0.006 x

\frac{d}{d x} (1 0^{- 8} x^{3}) = \frac{3 x ^{2}}{100000000}

= 500 - 0.006 x + \frac{3 x ^{2}}{100000000}

簡素化

= 500 - 0.006 x + 0.00000003 x^{2}