derivative f(t)=\sqrt[3]{t}

Lösung

ableitung von

f (t) = 3 t

\frac{1}{3 t ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d t} (3 t)

Wende Radikal Regel an:

n a = a^{\frac{1}{n}}

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

Wende die Potenzregel an:

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

= \frac{1}{3} t^{\frac{1}{3} - 1}

Vereinfache

\frac{1}{3} t^{\frac{1}{3} - 1} : \frac{1}{3 t ^{\frac{2}{3}}}

= \frac{1}{3 t ^{\frac{2}{3}}}

\int_{0}^{8} \frac{1}{64 + x ^{2}} d x

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