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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int_{0}^{1} 5 x - 5 x^{2} d x

in v erse l a pl a ce \frac{( s + 1 ) ^{2}}{s ^{2} - s - 6}

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

\frac{d}{d x} (sin (14 x))

y^{^{'}} = 1 + y^{2} + x + x y^{2}