derivative of 1/(x*ln(x))

Lösung

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

so l v e f or f, tan (f) (x) = \frac{x + 1}{x ^{3}}

im pl i c i t 3 x^{2} + x y + 3 y^{2} = 7

\int_{1}^{2} 8 x^{3} + 3 x^{2} d x

\frac{\partial}{\partial x} (1 + e^{2 x})

\int_{- 1}^{3} (t + 2) (t^{2} - 2 t + 4) d t