de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative f(x)=6x^{ln(x)}

Lösung

ableitung von

f (x) = 6 x^{l n (x)}

Lösung

\frac{12 e ^{l n^{2} (x)} ln ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (6 x^{l n (x)})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \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)}

= 6 \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}

= 6 e^{l n (x) l n (x)} \frac{2 ln ( x )}{x}

Vereinfache

6 e^{l n (x) l n (x)} \frac{2 ln ( x )}{x} : \frac{12 e ^{l n^{2} (x)} ln ( x )}{x}

= \frac{12 e ^{l n^{2} (x)} ln ( x )}{x}

Graph

Beliebte Beispiele

derivative-5/(x^3)

d er i v a t i v e - \frac{5}{x ^{3}}

derivative f(x)=sqrt(3x+5)

d er i v a t i v e f (x) = 3 x + 5

integral of cos^2(wt-kx)

\int cos^{2} (wt - k x) d x

integral of 1/(x^2-4)

\int \frac{1}{x ^{2} - 4} d x

limit as x approaches 0+of log_{2}(x)

x \to 0 + lim (lo g_{2} (x))