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人気のある微分積分 >

d/(dt)(t^ne^{at})

解

\frac{d}{d t} (t^{n} e^{a t})

解

n t^{n - 1} e^{a t} + e^{a t} a t^{n}

解答ステップ

\frac{d}{d t} (t^{n} e^{a t})

積の法則を適用:

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

f = t^{n}, g = e^{a t}

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

\frac{d}{d t} (t^{n}) = n t^{n - 1}

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

= n t^{n - 1} e^{a t} + e^{a t} a t^{n}

グラフ

人気の例

integral of (3x+4)^2

\int (3 x + 4)^{2} d x

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x \to 2 lim (\frac{∣ x - 2 ∣}{2 - x})

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x \to 0 lim (- 2 x^{2})

inverselaplace 2/(s(s+2)(s+3))

in v erse l a pl a ce \frac{2}{s ( s + 2 ) ( s + 3 )}

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