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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int x^{5} e^{3 x} d x

d er i v a t i v e f (x) = (x + 3)^{2}

\int_{\frac{1}{2}}^{1} (x^{- 3} - 2) d x

t an g e n t y = 6 x e^{x}, (0, 0)

d er i v a t i v e cos (4 t)