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

解

導関数

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

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

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (2 x^{3} + 4) = 6 x^{2}

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

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

簡素化

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

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