derivative x^3-6x^2-15x+4

解

導関数

x^{3} - 6 x^{2} - 15 x + 4

3 x^{2} - 12 x - 15

解答ステップ

\frac{d}{d x} (x^{3} - 6 x^{2} - 15 x + 4)

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} (15 x) + \frac{d}{d x} (4)

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

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

\frac{d}{d x} (15 x) = 15

\frac{d}{d x} (4) = 0

= 3 x^{2} - 12 x - 15 + 0

簡素化

= 3 x^{2} - 12 x - 15