d/(dt)((x)(80cos(x)+20))

解

\frac{d}{d t} ((t) (80 cos (t) + 20))

80 cos (t) + 20 - 80 t sin (t)

解答ステップ

\frac{d}{d t} ((t) (80 cos (t) + 20))

積の法則を適用:

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

f = t, g = 80 cos (t) + 20

= \frac{d t}{d t} (80 cos (t) + 20) + \frac{d}{d t} (80 cos (t) + 20) t

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

\frac{d}{d t} (80 cos (t) + 20) = - 80 sin (t)

= 1 \cdot (80 cos (t) + 20) + (- 80 sin (t)) t

簡素化

= 80 cos (t) + 20 - 80 t sin (t)