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人気のある微分積分 >

derivative of ln(x^2e^x)

解

\frac{d}{d x} (ln (x^{2} e^{x}))

解

\frac{2}{x} + 1

解答ステップ

\frac{d}{d x} (ln (x^{2} e^{x}))

簡素化

ln (x^{2} e^{x}) : ln (x^{2}) + x

= \frac{d}{d x} (ln (x^{2}) + x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x^{2})) + \frac{d x}{d x}

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

\frac{d x}{d x} = 1

= \frac{2}{x} + 1

グラフ

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