derivative of (x-10/(sqrt(x)-\sqrt{10)})

Lösung

\frac{d}{d x} (\frac{x - 10}{x - 10})

\frac{x - 2 10 x + 10}{2 x ( x - 10 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 10}{x - 10})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 10 ) ( x - 10 ) - \frac{d}{d x} ( x - 10 ) ( x - 10 )}{( x - 10 ) ^{2}}

\frac{d}{d x} (x - 10) = 1

\frac{d}{d x} (x - 10) = \frac{1}{2 x}

= \frac{1 \cdot ( x - 10 ) - \frac{1}{2 x} ( x - 10 )}{( x - 10 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 10 ) - \frac{1}{2 x} ( x - 10 )}{( x - 10 ) ^{2}} : \frac{x - 2 10 x + 10}{2 x ( x - 10 ) ^{2}}

= \frac{x - 2 10 x + 10}{2 x ( x - 10 ) ^{2}}