derivative of (4-2x(-x^3-2x^2+1))

解

\frac{d}{d x} ((4 - 2 x) (- x^{3} - 2 x^{2} + 1))

8 x^{3} - 16 x - 2

解答ステップ

\frac{d}{d x} ((4 - 2 x) (- x^{3} - 2 x^{2} + 1))

積の法則を適用:

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

f = 4 - 2 x, g = - x^{3} - 2 x^{2} + 1

= \frac{d}{d x} (4 - 2 x) (- x^{3} - 2 x^{2} + 1) + \frac{d}{d x} (- x^{3} - 2 x^{2} + 1) (4 - 2 x)

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

\frac{d}{d x} (- x^{3} - 2 x^{2} + 1) = - 3 x^{2} - 4 x

= (- 2) (- x^{3} - 2 x^{2} + 1) + (- 3 x^{2} - 4 x) (4 - 2 x)

簡素化

(- 2) (- x^{3} - 2 x^{2} + 1) + (- 3 x^{2} - 4 x) (4 - 2 x) : 8 x^{3} - 16 x - 2

= 8 x^{3} - 16 x - 2