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人気のある微分積分 >

d/(dt)(e^t*sin(t))

解

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

解

e^{t} sin (t) + cos (t) e^{t}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

= e^{t} sin (t) + cos (t) e^{t}

グラフ

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