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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

tangent f(x)=4-3ln(x),\at x=1

t an g e n t f (x) = 4 - 3 ln (x), at x = 1

derivative y=6+4sqrt(x)csc(x)

d er i v a t i v e y = 6 + 4 x csc (x)

sum from n=1 to infinity of 3/((4n^2-1))

n = 1 \sum \infty \frac{3}{( 4 n ^{2} - 1 )}

x y^{^{'}} = 2 y

sum from n=0 to infinity of-5

n = 0 \sum \infty - 5