d/(dt)(tcos(2t))

解

\frac{d}{d t} (t cos (2 t))

cos (2 t) - 2 t sin (2 t)

解答ステップ

\frac{d}{d t} (t cos (2 t))

積の法則を適用:

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

f = t, g = cos (2 t)

= \frac{d t}{d t} cos (2 t) + \frac{d}{d t} (cos (2 t)) t

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

\frac{d}{d t} (cos (2 t)) = - sin (2 t) \cdot 2

= 1 \cdot cos (2 t) + (- sin (2 t) \cdot 2) t

簡素化

= cos (2 t) - 2 t sin (2 t)