derivative of 48x^{1/2}

Lösung

\frac{d}{d x} (48 x^{\frac{1}{2}})

\frac{24}{x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} (48 x^{\frac{1}{2}})

Entferne die Konstante:

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

= 48 \frac{d}{d x} (x^{\frac{1}{2}})

Wende die Potenzregel an:

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

= 48 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Vereinfache

48 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{24}{x ^{\frac{1}{2}}}

= \frac{24}{x ^{\frac{1}{2}}}

f (x) = \frac{2}{ln ( x )}

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