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人気のある微分積分 >

derivative of (log_{e}(x)^2)

解

\frac{d}{d x} ((lo g_{e} (x))^{2})

解

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

解答ステップ

\frac{d}{d x} ((lo g_{e} (x))^{2})

簡素化

(lo g_{e} (x))^{2} : 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 of 70sin^4(x)cos^3(x)

\int 70 sin^{4} (x) cos^{3} (x) d x

integral from 1 to 2 of 4x^2

\int_{1}^{2} 4 x^{2} d x

limit as x approaches 5-of f(x)

x \to 5 - lim (f (x))

limit as x approaches 0 of (ln(x))/(x+1)

x \to 0 lim (\frac{ln ( x )}{x + 1})

tangent f(x)=(7x)/(x-3),\at x=6

t an g e n t f (x) = \frac{7 x}{x - 3}, at x = 6