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人気のある微分積分 >

derivative of xln(x^{15})

解

\frac{d}{d x} (x ln (x^{15}))

解

15 ln (x) + 15

解答ステップ

\frac{d}{d x} (x ln (x^{15}))

積の法則を適用:

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

f = x, g = ln (x^{15})

= \frac{d x}{d x} ln (x^{15}) + \frac{d}{d x} (ln (x^{15})) x

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

\frac{d}{d x} (ln (x^{15})) = \frac{15}{x}

= 1 \cdot ln (x^{15}) + \frac{15}{x} x

簡素化

1 \cdot ln (x^{15}) + \frac{15}{x} x : 15 ln (x) + 15

= 15 ln (x) + 15

グラフ

人気の例

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