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Beliebt Rechnen >

derivative f(x)=(2x^2)/(x^2-2x-8)

Lösung

ableitung von

f (x) = \frac{2 x ^{2}}{x ^{2} - 2 x - 8}

Lösung

\frac{2 ( - 2 x ^{2} - 16 x )}{( x ^{2} - 2 x - 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2}}{x ^{2} - 2 x - 8})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 2 x - 8})

Wende die Quotientenregel an:

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

= 2 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} - 2 x - 8 ) - \frac{d}{d x} ( x ^{2} - 2 x - 8 ) x ^{2}}{( x ^{2} - 2 x - 8 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 2 x - 8) = 2 x - 2

= 2 \cdot \frac{2 x ( x ^{2} - 2 x - 8 ) - ( 2 x - 2 ) x ^{2}}{( x ^{2} - 2 x - 8 ) ^{2}}

Vereinfache

2 \cdot \frac{2 x ( x ^{2} - 2 x - 8 ) - ( 2 x - 2 ) x ^{2}}{( x ^{2} - 2 x - 8 ) ^{2}} : \frac{2 ( - 2 x ^{2} - 16 x )}{( x ^{2} - 2 x - 8 ) ^{2}}

= \frac{2 ( - 2 x ^{2} - 16 x )}{( x ^{2} - 2 x - 8 ) ^{2}}

Graph

Beliebte Beispiele

integral of x/(x^2+2x)

\int \frac{x}{x ^{2} + 2 x} d x

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d er i v a t i v e (\frac{t ^{3}}{t ^{8} + 1})^{2}

y^{''}+4y=cos(t)

y^{^{''}} + 4 y = cos (t)

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x \to 6 lim (8 x^{2} - 3 x + 1)