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Beliebt Rechnen >

derivative (sqrt(x)-3)/(sqrt(x)+3)

Lösung

ableitung von

\frac{x - 3}{x + 3}

Lösung

\frac{3}{x ( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 3}{x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 3 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x - 3 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (x - 3) = \frac{1}{2 x}

\frac{d}{d x} (x + 3) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 3 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 3 )}{( x + 3 ) ^{2}} : \frac{3}{x ( x + 3 ) ^{2}}

= \frac{3}{x ( x + 3 ) ^{2}}

Graph

Beliebte Beispiele

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\int \frac{e ^{x}}{e ^{2 x} + 8 e ^{x} + 16} d x

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