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

Lösung

ableitung von

f (x) = ln (x x^{2} + 1)

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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