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人気のある微分積分 >

derivative of (ln(x)^{-1})

解

\frac{d}{d x} ((ln (x))^{- 1})

解

- \frac{1}{x ln ^{2} ( x )}

解答ステップ

\frac{d}{d x} ((ln (x))^{- 1})

連鎖法則を適用:

- \frac{1}{( ln ( x ) ) ^{2}} \frac{d}{d x} (ln (x))

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

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

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

簡素化

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

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

グラフ

人気の例

derivative y=x^{4/3}

d er i v a t i v e y = x^{\frac{4}{3}}

inverselaplace 1/(s^2-1)

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

integral from 0 to pi of cos(x)sin(x)

\int_{0}^{π} cos (x) sin (x) d x

integral from 0 to pi/6 of 64sin^2(x)

\int_{0}^{\frac{π}{6}} 64 sin^{2} (x) d x

integral of (cos(pi/(x^{31)}))/(x^{32)}

\int \frac{cos ( \frac{π}{x ^{31}} )}{x ^{32}} d x