derivative y=x^3-9x^2+24x-15

解

導関数

y = x^{3} - 9 x^{2} + 24 x - 15

3 x^{2} - 18 x + 24

解答ステップ

\frac{d}{d x} (x^{3} - 9 x^{2} + 24 x - 15)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (9 x^{2}) + \frac{d}{d x} (24 x) - \frac{d}{d x} (15)

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

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

\frac{d}{d x} (24 x) = 24

\frac{d}{d x} (15) = 0

= 3 x^{2} - 18 x + 24 - 0

簡素化

= 3 x^{2} - 18 x + 24