derivative of x/(sqrt(x-1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

\int \frac{4 x ^{2}}{x ^{2}} d x

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