derivative x^{2/3}(x-5)

Lösung

ableitung von

x^{\frac{2}{3}} (x - 5)

\frac{5 x - 10}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{2}{3}} (x - 5))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{2}{3}}, g = x - 5

= \frac{d}{d x} (x^{\frac{2}{3}}) (x - 5) + \frac{d}{d x} (x - 5) x^{\frac{2}{3}}

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

\frac{d}{d x} (x - 5) = 1

= \frac{2}{3 x ^{\frac{1}{3}}} (x - 5) + 1 \cdot x^{\frac{2}{3}}

Vereinfache

\frac{2}{3 x ^{\frac{1}{3}}} (x - 5) + 1 \cdot x^{\frac{2}{3}} : \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

= \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

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