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Beliebt Rechnen >

derivative f(x)=(2/3 x)^3

Lösung

ableitung von

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

Lösung

\frac{8 x ^{2}}{9}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (\frac{2}{3} x)^{2} \frac{2}{3} : \frac{8 x ^{2}}{9}

= \frac{8 x ^{2}}{9}

Graph

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