derivative f(3)=10+12x-3x^2-x^3

解

導関数

f (3) = 10 + 12 x - 3 x^{2} - x^{3}

- 3 x^{2} - 6 x + 12

解答ステップ

\frac{d}{d x} (10 + 12 x - 3 x^{2} - x^{3})

和/差の法則を適用:

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

= \frac{d}{d x} (10) + \frac{d}{d x} (12 x) - \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (x^{3})

\frac{d}{d x} (10) = 0

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

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

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

= 0 + 12 - 6 x - 3 x^{2}

簡素化

= - 3 x^{2} - 6 x + 12