derivative of x^3-6x^2+9x-1

解

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x - 1)

3 x^{2} - 12 x + 9

解答ステップ

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x - 1)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (9 x) - \frac{d}{d x} (1)

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

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (9 x) = 9

\frac{d}{d x} (1) = 0

= 3 x^{2} - 12 x + 9 - 0

簡素化

= 3 x^{2} - 12 x + 9