derivative of ln((sqrt(a^2-x^2)/x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 3 lim (2 x^{2} + 1)

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

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

d er i v a t i v e y = 3 + 9 - (x - 3)^{2}

d er i v a t i v e f (x) = \frac{4}{5 x + 1}