derivative 1/(x+xln(x))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x + x ln (x)) = ln (x) + 2

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

Vereinfache

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

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

d er i v a t i v e f (x) = (4 x^{2} + 3) (4 x - 5)

\frac{d}{d x} (ln (25))

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