(2x^{3/2})^'

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

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