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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{4 x}{( x - 2 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ( x - 2 ) ^{2} - 2 ( x - 2 ) x ^{2}}{( ( x - 2 ) ^{2} ) ^{2}} : - \frac{4 x}{( x - 2 ) ^{3}}

= - \frac{4 x}{( x - 2 ) ^{3}}

Graph

Beliebte Beispiele

derivative 7x\sqrt[3]{x}

d er i v a t i v e 7 x 3 x

integral of x(x^3+1)

\int x (x^{3} + 1) d x

fläche x+1,3-x^2

a re a x + 1, 3 - x^{2}

(dy)/(dx)+2y=90

\frac{d y}{d x} + 2 y = 90

limit as x approaches 3 of sec((pix)/3)

x \to 3 lim (sec (\frac{π x}{3}))