derivative of ln((x+2/(x-2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t an g e n t f (x) = 5 x, at x = 5

\int tan (5 x) sec^{2} (5 x) d x

a re a x - 2, x, [0, 4]

d er i v a t i v e [x + (x + sin^{2} (x))^{7}]^{5}

\int x 1 + 2 x^{2} d x