derivative of ((sqrt(x)-7)/(sqrt(x)+7))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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