derivative of 1/(ln^2(x))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{1}{x 9 x ^{2} + 16} d x

\int t^{2} t^{3} + 1 d t

\int \frac{r ^{3}}{4 + r ^{2}} d r

x \to 2 - lim (\frac{1 - x}{x - 2})

x y^{^{'}} - 2 y = 12 x^{2}