d/(dt)(e^{2t}cos(2t))

解

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

2 e^{2 t} cos (2 t) - 2 e^{2 t} sin (2 t)

解答ステップ

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

積の法則を適用:

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

f = e^{2 t}, g = cos (2 t)

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

\frac{d}{d t} (e^{2 t}) = e^{2 t} \cdot 2

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

= e^{2 t} \cdot 2 cos (2 t) + (- sin (2 t) \cdot 2) e^{2 t}

簡素化

= 2 e^{2 t} cos (2 t) - 2 e^{2 t} sin (2 t)