derivative f(x)=(2x-x^3)(3x+7)

解

導関数

f (x) = (2 x - x^{3}) (3 x + 7)

- 12 x^{3} - 21 x^{2} + 12 x + 14

解答ステップ

\frac{d}{d x} ((2 x - x^{3}) (3 x + 7))

積の法則を適用:

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

f = 2 x - x^{3}, g = 3 x + 7

= \frac{d}{d x} (2 x - x^{3}) (3 x + 7) + \frac{d}{d x} (3 x + 7) (2 x - x^{3})

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

\frac{d}{d x} (3 x + 7) = 3

= (2 - 3 x^{2}) (3 x + 7) + 3 (2 x - x^{3})

簡素化

(2 - 3 x^{2}) (3 x + 7) + 3 (2 x - x^{3}) : - 12 x^{3} - 21 x^{2} + 12 x + 14

= - 12 x^{3} - 21 x^{2} + 12 x + 14