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Beliebt Rechnen >

(1/(xln(x)))^'

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

(x ln (x))^{'} = ln (x) + 1

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative (2x^2+6x+4)/(sqrt(x))

d er i v a t i v e \frac{2 x ^{2} + 6 x + 4}{x}

derivative of (ln(3x)/(7x^2))

\frac{d}{d x} (\frac{ln ( 3 x )}{7 x ^{2}})

tangent f(x)= 1/x

t an g e n t f (x) = \frac{1}{x}

limit as x approaches-8 of (x-8)/(|x+8|)

x \to - 8 lim (\frac{x - 8}{∣ x + 8 ∣})

integral of 1/(x(ln(x))^pi)

\int \frac{1}{x ( ln ( x ) ) ^{π}} d x