derivative of 13/3 x^3+21/2 x^2-10x-7

解

\frac{d}{d x} (\frac{13}{3} x^{3} + \frac{21}{2} x^{2} - 10 x - 7)

13 x^{2} + 21 x - 10

解答ステップ

\frac{d}{d x} (\frac{13}{3} x^{3} + \frac{21}{2} x^{2} - 10 x - 7)

簡素化

\frac{13}{3} x^{3} + \frac{21}{2} x^{2} - 10 x - 7 : \frac{13 x ^{3}}{3} + \frac{21 x ^{2}}{2} - 10 x - 7

= \frac{d}{d x} (\frac{13 x ^{3}}{3} + \frac{21 x ^{2}}{2} - 10 x - 7)

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{13 x ^{3}}{3}) + \frac{d}{d x} (\frac{21 x ^{2}}{2}) - \frac{d}{d x} (10 x) - \frac{d}{d x} (7)

\frac{d}{d x} (\frac{13 x ^{3}}{3}) = 13 x^{2}

\frac{d}{d x} (\frac{21 x ^{2}}{2}) = 21 x

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

\frac{d}{d x} (7) = 0

= 13 x^{2} + 21 x - 10 - 0

簡素化

= 13 x^{2} + 21 x - 10