derivative of 2x^3-9x^2+12x-3

解

\frac{d}{d x} (2 x^{3} - 9 x^{2} + 12 x - 3)

6 x^{2} - 18 x + 12

解答ステップ

\frac{d}{d x} (2 x^{3} - 9 x^{2} + 12 x - 3)

和/差の法則を適用:

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

= \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (9 x^{2}) + \frac{d}{d x} (12 x) - \frac{d}{d x} (3)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (9 x^{2}) = 18 x

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

\frac{d}{d x} (3) = 0

= 6 x^{2} - 18 x + 12 - 0

簡素化

= 6 x^{2} - 18 x + 12