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人気のある微分積分 >

derivative of ln(x*ln(x))

解

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

解

\frac{2 ln ( x )}{x}

解答ステップ

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

簡素化

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

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

連鎖法則を適用:

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

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

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

= 2 ln (x) \frac{1}{x}

簡素化

2 ln (x) \frac{1}{x} : \frac{2 ln ( x )}{x}

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

グラフ

人気の例

integral from-1 to 1 of x/(x^2+x-6)

\int_{- 1}^{1} \frac{x}{x ^{2} + x - 6} d x

integral of (x^2)/(sqrt(256-x^2))

\int \frac{x ^{2}}{256 - x ^{2}} d x

(tan^{2} (x))^{^{'}}

limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5)

x \to 5 lim (\frac{( 13 - 4 x ^{2} + 69 )}{x - 5})

面積 y=-x+4,y=x^2+3x

a re a y = - x + 4, y = x^{2} + 3 x