d/(dt)(e^{4t}sin(t))

解

\frac{d}{d t} (e^{4 t} sin (t))

e^{4 t} \cdot 4 sin (t) + cos (t) e^{4 t}

解答ステップ

\frac{d}{d t} (e^{4 t} sin (t))

積の法則を適用:

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

f = e^{4 t}, g = sin (t)

= \frac{d}{d t} (e^{4 t}) sin (t) + \frac{d}{d t} (sin (t)) e^{4 t}

\frac{d}{d t} (e^{4 t}) = e^{4 t} \cdot 4

\frac{d}{d t} (sin (t)) = cos (t)

= e^{4 t} \cdot 4 sin (t) + cos (t) e^{4 t}