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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 0 lim (\frac{∣ - 2 x ∣}{5 x})

\frac{\partial}{\partial x} (34)

\int_{0}^{4} π e^{- \frac{x}{2}} d x

x \to 0 lim (2^{(x - 1)})

in v erse l a pl a ce \frac{4}{s + 5}