derivative of sqrt(ln(3x))

Lösung

\frac{d}{d x} (ln (3 x))

\frac{1}{2 x ln ( 3 x )}

Schritte zur Lösung

\frac{d}{d x} (ln (3 x))

Wende die Kettenregel an:

\frac{1}{2 ln ( 3 x )} \frac{d}{d x} (ln (3 x))

= \frac{1}{2 ln ( 3 x )} \frac{d}{d x} (ln (3 x))

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= \frac{1}{2 ln ( 3 x )} \cdot \frac{1}{x}

Vereinfache

\frac{1}{2 ln ( 3 x )} \cdot \frac{1}{x} : \frac{1}{2 x ln ( 3 x )}

= \frac{1}{2 x ln ( 3 x )}