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Beliebt Rechnen >

derivative f(x)=(x^2)/(x-1)

Lösung

ableitung von

f (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

tangent 4(8x-1)^4

t an g e n t 4 (8 x - 1)^{4}

x^{''}+4x^'+4x=e^{-2t}

x^{^{''}} + 4 x^{^{'}} + 4 x = e^{- 2 t}

derivative f(x)=3sqrt(x^3)

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

integral from 0 to 8 of-x^2+2x+4

\int_{0}^{8} - x^{2} + 2 x + 4 d x

tangent f(x)=(4x)/(x+1),\at x=3

t an g e n t f (x) = \frac{4 x}{x + 1}, at x = 3