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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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