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

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (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 )}

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

\int x sec^{2} (5 x) d x

y^{^{''}} + 4 y = - 2

y^{'} = 0.027 y (1 - \frac{y}{1527})

y^{^{''}} - 5 y^{^{'}} = 10 x + 3