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人気のある微分積分 >

derivative sqrt(w)e^w

解

導関数

w e^{w}

解

\frac{e ^{w}}{2 w} + e^{w} w

解答ステップ

\frac{d}{d w} (w e^{w})

積の法則を適用:

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

f = w, g = e^{w}

= \frac{d}{d w} (w) e^{w} + \frac{d}{d w} (e^{w}) w

\frac{d}{d w} (w) = \frac{1}{2 w}

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

= \frac{1}{2 w} e^{w} + e^{w} w

\frac{1}{2 w} e^{w} = \frac{e ^{w}}{2 w}

= \frac{e ^{w}}{2 w} + e^{w} w

グラフ

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