derivative x^3-8x^2+19x-12

解

導関数

x^{3} - 8 x^{2} + 19 x - 12

3 x^{2} - 16 x + 19

解答ステップ

\frac{d}{d x} (x^{3} - 8 x^{2} + 19 x - 12)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (8 x^{2}) + \frac{d}{d x} (19 x) - \frac{d}{d x} (12)

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

\frac{d}{d x} (8 x^{2}) = 16 x

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

\frac{d}{d x} (12) = 0

= 3 x^{2} - 16 x + 19 - 0

簡素化

= 3 x^{2} - 16 x + 19