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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

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

\frac{d}{d x} (7 + x) = 1

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

Vereinfache

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

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

Graph

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