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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

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

\frac{d}{d x} (x^{2} + 1) = 2 x

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

Vereinfache

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

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

Graph

Beliebte Beispiele

sum from n=1 to infinity of (1/6)^n

n = 1 \sum \infty (\frac{1}{6})^{n}

tangent x^2+8x-7

t an g e n t x^{2} + 8 x - 7

derivative (9x)/(2^x)

d er i v a t i v e \frac{9 x}{2 ^{x}}

derivative y=sqrt(4x^2+2)

d er i v a t i v e y = 4 x^{2} + 2

limit as x approaches-2 of (x^2-3)/(x+2)

x \to - 2 lim (\frac{x ^{2} - 3}{x + 2})