derivative of ln((x+1/(sqrt(x-1))))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

d er i v a t i v e 2 cos (2 t)

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

\int \frac{1}{6 x lo g _{7} ( x )} d x

\int 3 x^{2} y + e^{y} d x