derivative of 3x^4-2x^3+1

解

\frac{d}{d x} (3 x^{4} - 2 x^{3} + 1)

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

解答ステップ

\frac{d}{d x} (3 x^{4} - 2 x^{3} + 1)

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

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

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

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

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

簡素化

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