derivative ln(x/(x^2+1))

Lösung

ableitung von

ln (\frac{x}{x ^{2} + 1})

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

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 1}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )}

x y^{^{'}} - y = \frac{x ^{2}}{y ^{2}}

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

l a pl a ce t r an s f or m 25

a re a 4 - x^{2}, 3 x