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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\int e^{- t} \cdot (- t^{2} + t - 1) d t

\int_{0}^{4} (2 + x x) d x

\int 2 (1 - x) d x

\frac{d}{d y} (e^{y})