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Beliebt Rechnen >

derivative f(x)=ln(x^3-1)

Lösung

ableitung von

f (x) = ln (x^{3} - 1)

Lösung

\frac{3 x ^{2}}{x ^{3} - 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{x ^{3} - 1} \cdot 3 x^{2}

Vereinfache

\frac{1}{x ^{3} - 1} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} - 1}

= \frac{3 x ^{2}}{x ^{3} - 1}

Graph

Beliebte Beispiele

derivative of sqrt(x)+7/(sqrt(x))

\frac{d}{d x} (x + \frac{7}{x})

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limit as x approaches 5 of (3+1/x)^3

x \to 5 lim ((3 + \frac{1}{x})^{3})

y^{^{'}} = \frac{4 x}{e ^{x}}

derivative x^2(1-9x)

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