derivative of 7/3 x^3-2x^2+10

解

\frac{d}{d x} (\frac{7}{3} x^{3} - 2 x^{2} + 10)

7 x^{2} - 4 x

解答ステップ

\frac{d}{d x} (\frac{7}{3} x^{3} - 2 x^{2} + 10)

簡素化

\frac{7}{3} x^{3} - 2 x^{2} + 10 : \frac{7 x ^{3}}{3} - 2 x^{2} + 10

= \frac{d}{d x} (\frac{7 x ^{3}}{3} - 2 x^{2} + 10)

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{7 x ^{3}}{3}) - \frac{d}{d x} (2 x^{2}) + \frac{d}{d x} (10)

\frac{d}{d x} (\frac{7 x ^{3}}{3}) = 7 x^{2}

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

\frac{d}{d x} (10) = 0

= 7 x^{2} - 4 x + 0

簡素化

= 7 x^{2} - 4 x