derivative of ln(sqrt((x+9/(x-9))))

Lösung

\frac{d}{d x} (ln (\frac{x + 9}{x - 9}))

- \frac{9}{( x - 9 ) ( x + 9 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x + 9}{x - 9}))

Wende die Kettenregel an:

\frac{1}{\frac{x + 9}{x - 9}} \frac{d}{d x} (\frac{x + 9}{x - 9})

= \frac{1}{\frac{x + 9}{x - 9}} \frac{d}{d x} (\frac{x + 9}{x - 9})

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

= \frac{1}{\frac{x + 9}{x - 9}} (- \frac{9}{x + 9 ( x - 9 ) ^{\frac{3}{2}}})

Vereinfache

\frac{1}{\frac{x + 9}{x - 9}} (- \frac{9}{x + 9 ( x - 9 ) ^{\frac{3}{2}}}) : - \frac{9}{( x - 9 ) ( x + 9 )}

= - \frac{9}{( x - 9 ) ( x + 9 )}

\int \frac{( 5 x ^{3} - 3 5 x )}{5 x} d x

\frac{d}{d x} (arctan (3 x))

in v erse l a pl a ce \frac{s - 3}{4 s ^{2} + s + 12}

\int_{0}^{25} (- 12 x) d x

s l o p e (- 5, - 8), (- 1, 4)