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Beliebt Rechnen >

derivative of ln(sqrt(x^3))

Lösung

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

Lösung

\frac{3}{2 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{3}{2 x}

Graph

Beliebte Beispiele

derivative of (1/2 x^5)

\frac{d}{d x} ((\frac{1}{2} x)^{5})

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x \to \infty lim ((x)^{\frac{l n ( 2 )}{1 + l n ( x )}})

derivative f(x)=(100)/((1+5x)^3)

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\int x^{3} + sin (x) + cos (x) d x

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\int e^{8 x} sin (9 x) d x