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Beliebt Rechnen >

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

Lösung

ableitung von

f (x) = 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

integral of 5^tsin(5^t)

\int 5^{t} sin (5^{t}) d t

sum from n=1 to infinity of (n/(n+10))^n

n = 1 \sum \infty (\frac{n}{n + 10})^{n}

integral of cos^2(u)

\int cos^{2} (u) d u

integral from 0 to 25 of sqrt(x)

\int_{0}^{25} x d x

xy^'=x^3+17x^3y

x y^{^{'}} = x^{3} + 17 x^{3} y