derivative of ln((x^{1/2}/3))

Lösung

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

\frac{1}{2 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{3}) = \frac{1}{6 x ^{\frac{1}{2}}}

= \frac{1}{\frac{x ^{\frac{1}{2}}}{3}} \cdot \frac{1}{6 x ^{\frac{1}{2}}}

Vereinfache

\frac{1}{\frac{x ^{\frac{1}{2}}}{3}} \cdot \frac{1}{6 x ^{\frac{1}{2}}} : \frac{1}{2 x}

= \frac{1}{2 x}

\int (x^{2} - 3) d x

t an g e n t f (x) = ln (x^{3})

l a pl a ce t r an s f or m 3 e^{3 t}

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

\int e^{u} sin (u) d u