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Beliebt Rechnen >

derivative of ln(sqrt(((x-4)/(x-3))))

Lösung

\frac{d}{d x} (ln (\frac{( x - 4 )}{x - 3}))

Lösung

\frac{1}{2 ( x - 3 ) ( x - 4 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{( x - 4 )}{x - 3}))

Wende die Kettenregel an:

\frac{1}{\frac{x - 4}{x - 3}} \frac{d}{d x} (\frac{x - 4}{x - 3})

= \frac{1}{\frac{x - 4}{x - 3}} \frac{d}{d x} (\frac{x - 4}{x - 3})

\frac{d}{d x} (\frac{x - 4}{x - 3}) = \frac{1}{2 x - 4 ( x - 3 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x - 4}{x - 3}} \cdot \frac{1}{2 x - 4 ( x - 3 ) ^{\frac{3}{2}}}

Vereinfache

\frac{1}{\frac{x - 4}{x - 3}} \cdot \frac{1}{2 x - 4 ( x - 3 ) ^{\frac{3}{2}}} : \frac{1}{2 ( x - 3 ) ( x - 4 )}

= \frac{1}{2 ( x - 3 ) ( x - 4 )}

Graph

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