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Beliebt Rechnen >

derivative of (3x^{1/2}/2)

Lösung

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

Lösung

\frac{3}{4 x ^{\frac{1}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

\frac{3}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3}{4 x ^{\frac{1}{2}}}

= \frac{3}{4 x ^{\frac{1}{2}}}

Graph

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