derivative 2/3 x^3+x^2-12x+12

解

導関数

\frac{2}{3} x^{3} + x^{2} - 12 x + 12

2 x^{2} + 2 x - 12

解答ステップ

\frac{d}{d x} (\frac{2}{3} x^{3} + x^{2} - 12 x + 12)

簡素化

\frac{2}{3} x^{3} + x^{2} - 12 x + 12 : \frac{2 x ^{3}}{3} + x^{2} - 12 x + 12

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

和/差の法則を適用:

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

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

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

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

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (12) = 0

= 2 x^{2} + 2 x - 12 + 0

簡素化

= 2 x^{2} + 2 x - 12