derivative y=ln(8+ln(x))

Lösung

ableitung von

y = ln (8 + ln (x))

\frac{1}{x ( 8 + ln ( x ) )}

Schritte zur Lösung

\frac{d}{d x} (ln (8 + ln (x)))

Wende die Kettenregel an:

\frac{1}{8 + ln ( x )} \frac{d}{d x} (8 + ln (x))

= \frac{1}{8 + ln ( x )} \frac{d}{d x} (8 + ln (x))

\frac{d}{d x} (8 + ln (x)) = \frac{1}{x}

= \frac{1}{8 + ln ( x )} \cdot \frac{1}{x}

Vereinfache

\frac{1}{8 + ln ( x )} \cdot \frac{1}{x} : \frac{1}{x ( 8 + ln ( x ) )}

= \frac{1}{x ( 8 + ln ( x ) )}

\int \frac{1}{x ^{2} - 196} d x

x \to 0 + lim (ln (\frac{1}{5 x}))

\int sin (x) cos (x) 1 + cos^{2} (x) d x

x \to 0 lim (e^{- 7 x})

\frac{d}{d x} (\frac{e ^{2 x} - 1}{e ^{2 x} + 1})