(\partial}{\partial x}(\frac{10\sqrt[3]{(5x)^2})/3)

Lösung

\frac{\partial}{\partial x} \frac{10 3 ( 5 x ) ^{2}}{3}

\frac{20 \cdot 5 ^{\frac{2}{3}}}{9 3 x}

Schritte zur Lösung

\frac{\partial}{\partial x} \frac{10 3 ( 5 x ) ^{2}}{3}

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{10}{3} \frac{\partial}{\partial x} (3 (5 x)^{2})

Wende die Kettenregel an:

\frac{1}{3 ( ( 5 x ) ^{2} ) ^{\frac{2}{3}}} \frac{\partial}{\partial x} ((5 x)^{2})

= \frac{1}{3 ( ( 5 x ) ^{2} ) ^{\frac{2}{3}}} \frac{\partial}{\partial x} ((5 x)^{2})

\frac{\partial}{\partial x} ((5 x)^{2}) = 50 x

= \frac{10}{3} \cdot \frac{1}{3 ( ( 5 x ) ^{2} ) ^{\frac{2}{3}}} \cdot 50 x

Vereinfache

\frac{10}{3} \cdot \frac{1}{3 ( ( 5 x ) ^{2} ) ^{\frac{2}{3}}} \cdot 50 x : \frac{20 \cdot 5 ^{\frac{2}{3}}}{9 3 x}

= \frac{20 \cdot 5 ^{\frac{2}{3}}}{9 3 x}

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