derivative of ln(5+ln(x))

Lösung

\frac{d}{d x} (ln (5 + ln (x)))

\frac{1}{x ( 5 + ln ( x ) )}

Schritte zur Lösung

\frac{d}{d x} (ln (5 + ln (x)))

Wende die Kettenregel an:

\frac{1}{5 + ln ( x )} \frac{d}{d x} (5 + ln (x))

= \frac{1}{5 + ln ( x )} \frac{d}{d x} (5 + ln (x))

\frac{d}{d x} (5 + ln (x)) = \frac{1}{x}

= \frac{1}{5 + ln ( x )} \cdot \frac{1}{x}

Vereinfache

\frac{1}{5 + ln ( x )} \cdot \frac{1}{x} : \frac{1}{x ( 5 + ln ( x ) )}

= \frac{1}{x ( 5 + ln ( x ) )}

x \to \infty lim (5 e^{x})

\frac{\partial}{\partial x} (7 x^{6 y})

\frac{\partial}{\partial b} ((a x + b - y)^{2})

\int e^{\frac{- x}{3}} cos (5 x) d x

x \to 0 lim (\frac{11 sin ( 8 x )}{x})