derivative x(10-2x)(16-2x)

解

導関数

x (10 - 2 x) (16 - 2 x)

12 x^{2} - 104 x + 160

解答ステップ

\frac{d}{d x} (x (10 - 2 x) (16 - 2 x))

積の法則を適用:

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

f = x, g = (10 - 2 x) (16 - 2 x)

= \frac{d x}{d x} (10 - 2 x) (16 - 2 x) + \frac{d}{d x} ((10 - 2 x) (16 - 2 x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((10 - 2 x) (16 - 2 x)) = 8 x - 52

= 1 \cdot (10 - 2 x) (16 - 2 x) + (8 x - 52) x

簡素化

1 \cdot (10 - 2 x) (16 - 2 x) + (8 x - 52) x : 12 x^{2} - 104 x + 160

= 12 x^{2} - 104 x + 160