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Beliebt Rechnen >

derivative of ln(x^3-1/x)

Lösung

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

Lösung

\frac{3 x ^{4} + 1}{x ( x ^{4} - 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{x ^{3} - \frac{1}{x}} (3 x^{2} + \frac{1}{x ^{2}}) : \frac{3 x ^{4} + 1}{x ( x ^{4} - 1 )}

= \frac{3 x ^{4} + 1}{x ( x ^{4} - 1 )}

Graph

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