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Beliebt Rechnen >

derivative of log_{e}(x^3)

Lösung

\frac{d}{d x} (lo g_{e} (x^{3}))

Lösung

\frac{3}{x}

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (x^{3}))

Vereinfache

lo g_{e} (x^{3}) : ln (x^{3})

= \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}) = 3 x^{2}

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

Vereinfache

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

= \frac{3}{x}

Graph

Beliebte Beispiele

integral from 0 to 2 of 1/8 (x+y)

\int_{0}^{2} \frac{1}{8} (x + y) d y

f (x) = e^{2 x} - 1

tangent y=x^3-2x^2+5,\at x=2

t an g e n t y = x^{3} - 2 x^{2} + 5, at x = 2

derivative ln(pi)

d er i v a t i v e ln (π)

limit as x approaches-0.1 of (sin(x))/x

x \to - 0.1 lim (\frac{sin ( x )}{x})