derivative of (x^3/3+(x^2)/2-2x+7)

解

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

x^{2} + x - 2

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

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

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

簡素化

= x^{2} + x - 2