derivative f(x)= 1/(xln(x))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d 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 )}

\int_{0}^{x} a^{2} - t^{2} d t

\frac{d}{d x} (x^{2} - 25)

t an g e n t sin (7 x) + cos (6 x), at \frac{π}{6}

d er i v a t i v e y = x^{2} 8 + x

n = 1 \sum \infty ln (\frac{1}{n + 1})