derivative (4x^{3/2})/x

Lösung

ableitung von

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

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{\frac{3}{2}}}{x})

Vereinfache

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

= \frac{d}{d x} (4 x^{\frac{1}{2}})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{\frac{1}{2}})

Wende die Potenzregel an:

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

= 4 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Vereinfache

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

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

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