(\partial)/(\partial x)((ln(x))^x)

Lösung

\frac{\partial}{\partial x} ((ln (x))^{x})

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

Schritte zur Lösung

\frac{\partial}{\partial x} ((ln (x))^{x})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

2 x \frac{d y}{d x} = 1 - y^{2}

\int_{0}^{1} t e^{- t} d t

x \frac{d y}{d x} = 2 y

y^{^{'}} = \frac{1}{e ^{y} - x}

\frac{d}{d x} (2 x + 2 y)