derivative log_{e}(log_{e}(x))

Lösung

ableitung von

lo g_{e} (lo g_{e} (x))

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

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (lo g_{e} (x)))

Vereinfache

lo g_{e} (lo g_{e} (x)) : ln (ln (x))

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{ln ( x )} \cdot \frac{1}{x}

Vereinfache

\frac{1}{ln ( x )} \cdot \frac{1}{x} : \frac{1}{x ln ( x )}

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

t an g e n t f (x) = x^{4} + 5 x^{2} - x, at x = 1

\frac{d}{d x} (\frac{1 - 4 x}{1 + 4 x})

\int ln (cos (x)) \cdot tan (x) d x

\frac{d}{d x} (\frac{4}{x} - x (x + 1))

n = 0 \sum \infty (- \frac{8}{9})^{n}