derivative of 0.006x^3+0.07x^2+18x+600

解

\frac{d}{d x} (0.006 x^{3} + 0.07 x^{2} + 18 x + 600)

0.018 x^{2} + 0.14 x + 18

解答ステップ

\frac{d}{d x} (0.006 x^{3} + 0.07 x^{2} + 18 x + 600)

和/差の法則を適用:

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

= \frac{d}{d x} (0.006 x^{3}) + \frac{d}{d x} (0.07 x^{2}) + \frac{d}{d x} (18 x) + \frac{d}{d x} (600)

\frac{d}{d x} (0.006 x^{3}) = 0.018 x^{2}

\frac{d}{d x} (0.07 x^{2}) = 0.14 x

\frac{d}{d x} (18 x) = 18

\frac{d}{d x} (600) = 0

= 0.018 x^{2} + 0.14 x + 18 + 0

簡素化

= 0.018 x^{2} + 0.14 x + 18