derivative ((sqrt(x)-2))/(sqrt(x)+3)

Lösung

ableitung von

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

\frac{5}{2 x ( x + 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

Vereinfache

\frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 2 )}{( x + 3 ) ^{2}} : \frac{5}{2 x ( x + 3 ) ^{2}}

= \frac{5}{2 x ( x + 3 ) ^{2}}

\frac{d}{d x} (3 x y)

in v erse l a pl a ce \frac{2 x}{( x ^{2} + 4 ) ^{2}}

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