derivative f(x)=(x^3)/3+4x^2+12x+19

解

導関数

f (x) = \frac{x ^{3}}{3} + 4 x^{2} + 12 x + 19

x^{2} + 8 x + 12

解答ステップ

\frac{d}{d x} (\frac{x ^{3}}{3} + 4 x^{2} + 12 x + 19)

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} (4 x^{2}) + \frac{d}{d x} (12 x) + \frac{d}{d x} (19)

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

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

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (19) = 0

= x^{2} + 8 x + 12 + 0

簡素化

= x^{2} + 8 x + 12