derivative of ln(1+a/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to + 3 lim (f (x))

in v erse l a pl a ce \frac{1}{s ( s + 2 )}

\int 13 (tan (x)) (ln (cos (x))) d x

x \to + \frac{π}{2} lim (cot (x))

d er i v a t i v e f (x) = 5 arcsin (x^{3})