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人気のある微分積分 >

derivative of xln(5x)

解

\frac{d}{d x} (x ln (5 x))

解

ln (5 x) + 1

解答ステップ

\frac{d}{d x} (x ln (5 x))

積の法則を適用:

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

f = x, g = ln (5 x)

= \frac{d x}{d x} ln (5 x) + \frac{d}{d x} (ln (5 x)) x

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= 1 \cdot ln (5 x) + \frac{1}{x} x

簡素化

1 \cdot ln (5 x) + \frac{1}{x} x : ln (5 x) + 1

= ln (5 x) + 1

グラフ

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