derivative f(x)=4x^3-11x^2-14x+19

解

導関数

f (x) = 4 x^{3} - 11 x^{2} - 14 x + 19

12 x^{2} - 22 x - 14

解答ステップ

\frac{d}{d x} (4 x^{3} - 11 x^{2} - 14 x + 19)

和/差の法則を適用:

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

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (11 x^{2}) - \frac{d}{d x} (14 x) + \frac{d}{d x} (19)

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

\frac{d}{d x} (11 x^{2}) = 22 x

\frac{d}{d x} (14 x) = 14

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

= 12 x^{2} - 22 x - 14 + 0

簡素化

= 12 x^{2} - 22 x - 14