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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

y^{^{''}} + 30 y = 0

integral of (2x)/(2x-1)

\int \frac{2 x}{2 x - 1} d x

integral of (2x^3-x+0)^3*(6x^2-1)

\int (2 x^{3} - x + 0)^{3} \cdot (6 x^{2} - 1) d x

derivative of 6^{sqrt(x)}

\frac{d}{d x} (6^{x})

limit as x approaches 0 of (1+x)^{1/x}

x \to 0 lim ((1 + x)^{\frac{1}{x}})