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

解

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

14 x^{6} - 16 x^{3} - 6

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x^{3} + 2, g = x^{4} - 3 x

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

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

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

= 6 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (2 x^{3} + 2)

簡素化

6 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (2 x^{3} + 2) : 14 x^{6} - 16 x^{3} - 6

= 14 x^{6} - 16 x^{3} - 6