derivative of ln(x^{ln(x}))

Lösung

\frac{d}{d x} (ln (x^{l n (x)}))

\frac{2 e ^{l n^{2} (x)} ln ( x )}{x ^{l n (x) + 1}}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{l n (x)}))

Wende die Kettenregel an:

\frac{1}{x ^{l n (x)}} \frac{d}{d x} (x^{l n (x)})

= \frac{1}{x ^{l n (x)}} \frac{d}{d x} (x^{l n (x)})

\frac{d}{d x} (x^{l n (x)}) = \frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

= \frac{1}{x ^{l n (x)}} \cdot \frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

Vereinfache

\frac{1}{x ^{l n (x)}} \cdot \frac{2 e ^{l n^{2} (x)} ln ( x )}{x} : \frac{2 e ^{l n^{2} (x)} ln ( x )}{x ^{l n (x) + 1}}

= \frac{2 e ^{l n^{2} (x)} ln ( x )}{x ^{l n (x) + 1}}

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