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人気のある微分積分 >

derivative e^t*sin(2t)

解

導関数

e^{t} \cdot sin (2 t)

解

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

グラフ

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