derivative of 2/3 x^3-4x^2+10x+6

解

\frac{d}{d x} (\frac{2}{3} x^{3} - 4 x^{2} + 10 x + 6)

2 x^{2} - 8 x + 10

解答ステップ

\frac{d}{d x} (\frac{2}{3} x^{3} - 4 x^{2} + 10 x + 6)

簡素化

\frac{2}{3} x^{3} - 4 x^{2} + 10 x + 6 : \frac{2 x ^{3}}{3} - 4 x^{2} + 10 x + 6

= \frac{d}{d x} (\frac{2 x ^{3}}{3} - 4 x^{2} + 10 x + 6)

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} (4 x^{2}) + \frac{d}{d x} (10 x) + \frac{d}{d x} (6)

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

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (10 x) = 10

\frac{d}{d x} (6) = 0

= 2 x^{2} - 8 x + 10 + 0

簡素化

= 2 x^{2} - 8 x + 10