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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

- \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}

Vereinfache

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

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

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

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

\int_{0}^{π} cos (x) sin (x) d x

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