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Beliebt Rechnen >

derivative of (7sqrt(x)/x)

Lösung

\frac{d}{d x} (\frac{7 x}{x})

Lösung

- \frac{7}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x}{x})

Entferne die Konstante:

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

= 7 \frac{d}{d x} (\frac{x}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 7 \cdot \frac{\frac{d}{d x} ( x ) x - \frac{d x}{d x} x}{x ^{2}}

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

\frac{d x}{d x} = 1

= 7 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

Vereinfache

7 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{7}{2 x ^{\frac{3}{2}}}

= - \frac{7}{2 x ^{\frac{3}{2}}}

Graph

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