derivative f(t)=t^{2/3}-t^{1/3}+4

Lösung

ableitung von

f (t) = t^{\frac{2}{3}} - t^{\frac{1}{3}} + 4

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

Schritte zur Lösung

\frac{d}{d t} (t^{\frac{2}{3}} - t^{\frac{1}{3}} + 4)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (t^{\frac{2}{3}}) - \frac{d}{d t} (t^{\frac{1}{3}}) + \frac{d}{d t} (4)

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

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

\frac{d}{d t} (4) = 0

= \frac{2}{3 t ^{\frac{1}{3}}} - \frac{1}{3 t ^{\frac{2}{3}}} + 0

Vereinfache

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

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