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Beliebt Rechnen >

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

Lösung

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

Lösung

\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}}

Graph

Beliebte Beispiele

derivative h(x)=(x+1)^7-7x-3

d er i v a t i v e h (x) = (x + 1)^{7} - 7 x - 3

integral of e^xcos(7x)

\int e^{x} cos (7 x) d x

fläche 2sqrt(x),x,2

a re a 2 x, x, 2

(\partial)/(\partial y)(cos(2y)-3x^2y^2)

\frac{\partial}{\partial y} (cos (2 y) - 3 x^{2} y^{2})

limit as x approaches 2-of 1/((1.9)-2)

x \to 2 - lim (\frac{1}{( 1.9 ) - 2})