derivative of ln(sqrt(x)-1)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{x - 1} \cdot \frac{1}{2 x}

Vereinfache

\frac{1}{x - 1} \cdot \frac{1}{2 x} : \frac{1}{2 x ( x - 1 )}

= \frac{1}{2 x ( x - 1 )}

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

d er i v a t i v e y = \frac{7}{ln ( x )}

\frac{d}{d x} (\frac{5 x}{6})

x \to 9 - lim (\frac{1}{x - 9})

x \to 0 + lim (x [ln (x)]^{2})