derivative of ln(xsqrt(x^2-4))

Lösung

\frac{d}{d x} (ln (x x^{2} - 4))

\frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

Schritte zur Lösung

\frac{d}{d x} (ln (x x^{2} - 4))

Wende die Kettenregel an:

\frac{1}{x x ^{2} - 4} \frac{d}{d x} (x x^{2} - 4)

= \frac{1}{x x ^{2} - 4} \frac{d}{d x} (x x^{2} - 4)

\frac{d}{d x} (x x^{2} - 4) = \frac{2 x ^{2} - 4}{x ^{2} - 4}

= \frac{1}{x x ^{2} - 4} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4}

Vereinfache

\frac{1}{x x ^{2} - 4} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4} : \frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

= \frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

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