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Beliebt Rechnen >

derivative f(x)=(x^2)/(x^2+2)

Lösung

ableitung von

f (x) = \frac{x ^{2}}{x ^{2} + 2}

Lösung

\frac{4 x}{( x ^{2} + 2 ) ^{2}}

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

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

Vereinfache

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

= \frac{4 x}{( x ^{2} + 2 ) ^{2}}

Graph

Beliebte Beispiele

\int 54

derivative (sqrt(x))^{5x}

d er i v a t i v e (x)^{5 x}

((x^2+1)dy)/(dx)+3x(y-1)=0

\frac{( x ^{2} + 1 ) d y}{d x} + 3 x (y - 1) = 0

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integral of 1/(2*sqrt(x))

\int \frac{1}{2 \cdot x} d x