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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

\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 )}

Graph

Beliebte Beispiele

derivative of 3^{2x-1}

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

integral of 1/((x^2-25)^2)

\int \frac{1}{( x ^{2} - 25 ) ^{2}} d x

tangent f(x)=x^2+5,\at x=5

t an g e n t f (x) = x^{2} + 5, at x = 5

limit as x approaches 3 of sqrt(2)

x \to 3 lim (2)

derivative of pi

\frac{d}{d x} (π)