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Beliebt Rechnen >

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

Lösung

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

Lösung

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of cos(cx)

\int cos (c x) d x

derivative of sin(pi/3)

\frac{d}{d x} (sin (\frac{π}{3}))

derivative of 3cos(x+4x^2)

\frac{d}{d x} (3 cos (x) + 4 x^{2})

x^4+5y^4sqrt(x^5+4)y^'=0,y(0)=1

x^{4} + 5 y^{4} x^{5} + 4 y^{^{'}} = 0, y (0) = 1

integral of (4x^4-5x^2)/((x+3)(x-2))

\int \frac{4 x ^{4} - 5 x ^{2}}{( x + 3 ) ( x - 2 )} d x