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Beliebt Rechnen >

derivative ln(x^2+1)

Lösung

ableitung von

ln (x^{2} + 1)

Lösung

\frac{2 x}{x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{x ^{2} + 1} \cdot 2 x

Vereinfache

\frac{1}{x ^{2} + 1} \cdot 2 x : \frac{2 x}{x ^{2} + 1}

= \frac{2 x}{x ^{2} + 1}

Graph

Beliebte Beispiele

derivative of ln(\sqrt[3]{x^3+8})

\frac{d}{d x} (ln (3 x^{3} + 8))

integral of (2x)/(sqrt(3x+1))

\int \frac{2 x}{3 x + 1} d x

integral of (e^x-26^x)

\int (e^{x} - 2 6^{x}) d x

derivative 3sqrt(25-x^2)

d er i v a t i v e 3 25 - x^{2}

derivative f(x)=(x^3+2x^2+x+2)/(x+2)

d er i v a t i v e f (x) = \frac{x ^{3} + 2 x ^{2} + x + 2}{x + 2}