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人気のある微分積分 >

d/(dt)(Ate^t)

解

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

解

A (e^{t} + e^{t} t)

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

f = t, g = e^{t}

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

\frac{d t}{d t} = 1

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

= A (1 \cdot e^{t} + e^{t} t)

簡素化

= A (e^{t} + e^{t} t)

グラフ

人気の例

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