derivative y=1.45e^{59.9t}sin(201t)

解

導関数

y = 1.45 e^{59.9 t} sin (201 t)

1.45 (e^{59.9 t} \cdot 59.9 sin (201 t) + cos (201 t) \cdot 201 e^{59.9 t})

解答ステップ

\frac{d}{d t} (1.45 e^{59.9 t} sin (201 t))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 1.45 \frac{d}{d t} (e^{59.9 t} sin (201 t))

積の法則を適用:

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

f = e^{59.9 t}, g = sin (201 t)

= 1.45 (\frac{d}{d t} (e^{59.9 t}) sin (201 t) + \frac{d}{d t} (sin (201 t)) e^{59.9 t})

\frac{d}{d t} (e^{59.9 t}) = e^{59.9 t} \cdot 59.9

\frac{d}{d t} (sin (201 t)) = cos (201 t) \cdot 201

= 1.45 (e^{59.9 t} \cdot 59.9 sin (201 t) + cos (201 t) \cdot 201 e^{59.9 t})