derivative y=ln(sqrt((x+1)/(x-1)))

Lösung

ableitung von

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

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

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

Vereinfache

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

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

l in e (- 2, 6), (3, - 2)

t an g e n t f (x) = x^{2}, at x = 1

y = 3 x

d er i v a t i v e f (x) = ln (sinh (x))

in t e g r a l sin (x)