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Beliebt Rechnen >

derivative of (x-5/(8sqrt(x)))

Lösung

\frac{d}{d x} (\frac{x - 5}{8 x})

Lösung

\frac{x + 5}{16 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 5}{8 x})

Entferne die Konstante:

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

= \frac{1}{8} \frac{d}{d x} (\frac{x - 5}{x})

Wende die Quotientenregel an:

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

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( x - 5 ) x - \frac{d}{d x} ( x ) ( x - 5 )}{( x ) ^{2}}

\frac{d}{d x} (x - 5) = 1

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

= \frac{1}{8} \cdot \frac{1 \cdot x - \frac{1}{2 x} ( x - 5 )}{( x ) ^{2}}

Vereinfache

\frac{1}{8} \cdot \frac{1 \cdot x - \frac{1}{2 x} ( x - 5 )}{( x ) ^{2}} : \frac{x + 5}{16 x x}

= \frac{x + 5}{16 x x}

Graph

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