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Beliebt Rechnen >

derivative ln(sqrt(((x-3))/(x-1)))

Lösung

ableitung von

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

Lösung

\frac{1}{( x - 1 ) ( x - 3 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{\frac{x - 3}{x - 1}} \frac{d}{d x} (\frac{x - 3}{x - 1})

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

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

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

Vereinfache

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

= \frac{1}{( x - 1 ) ( x - 3 )}

Graph

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