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Beliebt Rechnen >

derivative of ln(x^6-1)

Lösung

\frac{d}{d x} (ln (x^{6} - 1))

Lösung

\frac{6 x ^{5}}{x ^{6} - 1}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{6} - 1))

Wende die Kettenregel an:

\frac{1}{x ^{6} - 1} \frac{d}{d x} (x^{6} - 1)

= \frac{1}{x ^{6} - 1} \frac{d}{d x} (x^{6} - 1)

\frac{d}{d x} (x^{6} - 1) = 6 x^{5}

= \frac{1}{x ^{6} - 1} \cdot 6 x^{5}

Vereinfache

\frac{1}{x ^{6} - 1} \cdot 6 x^{5} : \frac{6 x ^{5}}{x ^{6} - 1}

= \frac{6 x ^{5}}{x ^{6} - 1}

Graph

Beliebte Beispiele

tangent y=x^3,(2,8)

t an g e n t y = x^{3}, (2, 8)

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\frac{\partial}{\partial x} ((x^{3} + x^{4}) (x^{2} + 3 x)^{2})

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\frac{d}{d x} ((3 x - 7)^{12})

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

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

f (x) = e^{x} + ln (x)