derivative of 1/3 x^3+7x^2+50x

解

\frac{d}{d x} (\frac{1}{3} x^{3} + 7 x^{2} + 50 x)

x^{2} + 14 x + 50

解答ステップ

\frac{d}{d x} (\frac{1}{3} x^{3} + 7 x^{2} + 50 x)

簡素化

\frac{1}{3} x^{3} + 7 x^{2} + 50 x : \frac{x ^{3}}{3} + 7 x^{2} + 50 x

= \frac{d}{d x} (\frac{x ^{3}}{3} + 7 x^{2} + 50 x)

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} (7 x^{2}) + \frac{d}{d x} (50 x)

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

\frac{d}{d x} (7 x^{2}) = 14 x

\frac{d}{d x} (50 x) = 50

= x^{2} + 14 x + 50