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

解

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

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

解答ステップ

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

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} (x^{2}) - \frac{d}{d x} (2)

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

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

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

\frac{d}{d x} (2) = 0

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

簡素化

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