derivative ln(sqrt((4x+1)/(x^2-1)))

Lösung

ableitung von

ln (\frac{4 x + 1}{x ^{2} - 1})

- \frac{2 x ^{2} + x + 2}{( x ^{2} - 1 ) ( 4 x + 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{4 x + 1}{x ^{2} - 1}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{0}^{5} \frac{w}{w - 2} d w

x \to 0 lim (3 x cos (x))

\frac{d}{d x} (\frac{1 + e ^{x}}{1 - e ^{x}})

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

d er i v a t i v e z e^{z}