derivative ln(sqrt(((x+2))/(x-2)))

Lösung

ableitung von

ln (\frac{( x + 2 )}{x - 2})

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

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x + 2}{x - 2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{\frac{x + 2}{x - 2}} (- \frac{2}{x + 2 ( x - 2 ) ^{\frac{3}{2}}}) : - \frac{2}{( x - 2 ) ( x + 2 )}

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