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Beliebt Rechnen >

derivative of 30sqrt(x)

Lösung

\frac{d}{d x} (30 x)

Lösung

\frac{15}{x}

Schritte zur Lösung

\frac{d}{d x} (30 x)

Entferne die Konstante:

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

= 30 \frac{d}{d x} (x)

Wende Radikal Regel an:

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

= 30 \frac{d}{d x} (x^{\frac{1}{2}})

Wende die Potenzregel an:

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

= 30 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Vereinfache

30 \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{15}{x}

= \frac{15}{x}

Graph

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