derivative of ln((x+1/(x-3)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

f (x) = \frac{5}{x ^{3}}

\int 8 u^{\frac{7}{2}} d u

t a y l or 5^{x}, 0

d er i v a t i v e y = (x^{4} + 2)^{2} (x^{5} + 4)^{4}

\frac{d}{d x} (e^{4} x^{7})