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Beliebt Rechnen >

derivative f(x)= x/(7-sqrt(x))

Lösung

ableitung von

f (x) = \frac{x}{7 - x}

Lösung

\frac{14 - x}{2 ( 7 - x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (7 - x) = - \frac{1}{2 x}

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

Vereinfache

\frac{1 \cdot ( 7 - x ) - ( - \frac{1}{2 x} ) x}{( 7 - x ) ^{2}} : \frac{14 - x}{2 ( 7 - x ) ^{2}}

= \frac{14 - x}{2 ( 7 - x ) ^{2}}

Graph

Beliebte Beispiele

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