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人気のある微分積分 >

derivative of ln(sqrt(x^3))

解

\frac{d}{d x} (ln (x^{3}))

解

\frac{3}{2 x}

解答ステップ

\frac{d}{d x} (ln (x^{3}))

連鎖法則を適用:

\frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

= \frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = \frac{3 x}{2}

= \frac{1}{x ^{3}} \cdot \frac{3 x}{2}

簡素化

\frac{1}{x ^{3}} \cdot \frac{3 x}{2} : \frac{3}{2 x}

= \frac{3}{2 x}

グラフ

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