derivative ln(sqrt((x-5)/(x-4)))

Lösung

ableitung von

ln (\frac{x - 5}{x - 4})

\frac{1}{2 ( x - 4 ) ( x - 5 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x - 5}{x - 4}))

Wende die Kettenregel an:

\frac{1}{\frac{x - 5}{x - 4}} \frac{d}{d x} (\frac{x - 5}{x - 4})

= \frac{1}{\frac{x - 5}{x - 4}} \frac{d}{d x} (\frac{x - 5}{x - 4})

\frac{d}{d x} (\frac{x - 5}{x - 4}) = \frac{1}{2 x - 5 ( x - 4 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x - 5}{x - 4}} \cdot \frac{1}{2 x - 5 ( x - 4 ) ^{\frac{3}{2}}}

Vereinfache

\frac{1}{\frac{x - 5}{x - 4}} \cdot \frac{1}{2 x - 5 ( x - 4 ) ^{\frac{3}{2}}} : \frac{1}{2 ( x - 4 ) ( x - 5 )}

= \frac{1}{2 ( x - 4 ) ( x - 5 )}

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

f^{^{'}} (x) = 2 sec (x) + 3 tan (x) - tan (\frac{π}{3})

y^{^{''}} + (\frac{1}{x}) y^{^{'}} = 0

y^{^{'}} = \frac{- ( x y + 1 )}{x y + 1}

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