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人気のある微分積分 >

derivative y=(ln(x))^3

解

導関数

y = (ln (x))^{3}

解

\frac{3 ln ^{2} ( x )}{x}

解答ステップ

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

連鎖法則を適用:

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

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

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

= 3 (ln (x))^{2} \frac{1}{x}

簡素化

3 ln^{2} (x) \frac{1}{x} : \frac{3 ln ^{2} ( x )}{x}

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

グラフ

人気の例

derivative f(x)=e^{2-x}

d er i v a t i v e f (x) = e^{2 - x}

tangent x^2+3,\at (x=1)

t an g e n t x^{2} + 3, at (x = 1)

inverselaplace (s^2-1)/(s^4+3s^2+2)

in v erse l a pl a ce \frac{s ^{2} - 1}{s ^{4} + 3 s ^{2} + 2}

integral of 1/(2x^2+2)

\int \frac{1}{2 x ^{2} + 2} d x

d er i v a t i v e - t