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

解

導関数

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

15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (3 x^{3} + 2 x) = 9 x^{2} + 2

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

= (9 x^{2} + 2) (x - 2) (x + 4) + (2 x + 2) (3 x^{3} + 2 x)

簡素化

(9 x^{2} + 2) (x - 2) (x + 4) + (2 x + 2) (3 x^{3} + 2 x) : 15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16

= 15 x^{4} + 24 x^{3} - 66 x^{2} + 8 x - 16