d/(dt)((w)((w-2)(w-3)))

解

\frac{d}{d t} ((t) ((t - 2) (t - 3)))

3 t^{2} - 10 t + 6

解答ステップ

\frac{d}{d t} ((t) ((t - 2) (t - 3)))

積の法則を適用:

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

f = t, g = (t - 2) (t - 3)

= \frac{d t}{d t} (t - 2) (t - 3) + \frac{d}{d t} ((t - 2) (t - 3)) t

\frac{d t}{d t} = 1

\frac{d}{d t} ((t - 2) (t - 3)) = 2 t - 5

= 1 \cdot (t - 2) (t - 3) + (2 t - 5) t

簡素化

1 \cdot (t - 2) (t - 3) + (2 t - 5) t : 3 t^{2} - 10 t + 6

= 3 t^{2} - 10 t + 6