derivative of 1/((ln(x)^3))

Lösung

\frac{d}{d x} (\frac{1}{( ln ( x ) ) ^{3}})

- \frac{3}{x ln ^{4} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( ln ( x ) ) ^{3}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

- \frac{3}{( ln ( x ) ) ^{4}} \frac{d}{d x} (ln (x))

= - \frac{3}{( ln ( x ) ) ^{4}} \frac{d}{d x} (ln (x))

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

= - \frac{3}{( ln ( x ) ) ^{4}} \cdot \frac{1}{x}

Vereinfache

- \frac{3}{ln ^{4} ( x )} \cdot \frac{1}{x} : - \frac{3}{x ln ^{4} ( x )}

= - \frac{3}{x ln ^{4} ( x )}

\int \frac{x ^{2} + 3}{x + 1} d x

\int \frac{1}{3 - 8 x - x ^{2}} d x

x \to 1 lim (\frac{x - 11}{x + 7})

\int \frac{1}{u 6 - u ^{2}} d u

\frac{d}{d x} (\frac{x ^{4}}{4} + \frac{1}{8 x ^{2}})