derivative f(x)=3x^4-12x^3+9

解

導関数

f (x) = 3 x^{4} - 12 x^{3} + 9

12 x^{3} - 36 x^{2}

解答ステップ

\frac{d}{d x} (3 x^{4} - 12 x^{3} + 9)

和/差の法則を適用:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (12 x^{3}) + \frac{d}{d x} (9)

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

\frac{d}{d x} (12 x^{3}) = 36 x^{2}

\frac{d}{d x} (9) = 0

= 12 x^{3} - 36 x^{2} + 0

簡素化

= 12 x^{3} - 36 x^{2}