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

Lösung

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

x^{l n (l n (x)) - 1} (ln (ln (x)) + 1)

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= x^{l n (l n (x)) - 1} (ln (ln (x)) + 1)

x \to 7 lim (\frac{x + 4}{x - 7})

d er i v a t i v e f (2) = \frac{x ^{2} - 4}{x - 2}

\frac{d ^{2} x}{d t ^{2}} = - k x

\frac{d}{d x} ((8 x^{2} - 2 x) (5 x + 9))

y^{^{''}} - 4 y^{^{'}} + 53 y = 0