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Beliebt Rechnen >

derivative of e^{ln(ln(2x)})

Lösung

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

Lösung

\frac{1}{x}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Kettenregel an:

\frac{1}{2 x} \frac{d}{d x} (2 x)

= \frac{1}{2 x} \frac{d}{d x} (2 x)

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

= \frac{1}{2 x} \cdot 2

Vereinfache

\frac{1}{2 x} \cdot 2 : \frac{1}{x}

= \frac{1}{x}

Graph

Beliebte Beispiele

limit as x approaches 2 of 4/((x-2)^2)

x \to 2 lim (\frac{4}{( x - 2 ) ^{2}})

derivative f(x)=322560(2x+5)

d er i v a t i v e f (x) = 322560 (2 x + 5)

(d^3)/(dx^3)(sqrt(x+1))

\frac{d ^{3}}{d x ^{3}} (x + 1)

sum from n=0 to infinity of (n!)/(5^n)

n = 0 \sum \infty \frac{n !}{5 ^{n}}

derivative of 8ysin(x)

\frac{d}{d x} (8 y sin (x))