(1/(x(ln(x))^2))^'

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

= ((x (ln (x))^{2})^{- 1})^{^{'}}

Wende die Kettenregel an:

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

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

(x (ln (x))^{2})^{'} = ln^{2} (x) + 2 ln (x)

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

Vereinfache

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

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

\frac{\partial}{\partial x} (\frac{x ^{2}}{2})

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

\int_{- 1}^{1} (3 x^{2} + 1)^{2} d x

\int \frac{- 4}{x ^{2}} d x

d er i v a t i v e y = \frac{2 x - 3}{4 x + 1}