derivative y=x^{ln(x)}

Lösung

ableitung von

y = x^{l n (x)}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{l n (x)} = e^{l n (x) l n (x)}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

p o l a r (- 6, 6)

d er i v a t i v e f (x) = e^{\frac{1}{x}}

mi d p o in t (7, - 12), (- 5, - 15)

c a r t es ian (- 3, - \frac{π}{6})

mi d p o in t (- 2, - 7), (7, 4)