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Beliebt Rechnen >

derivative of (x^2/(x^2-4))

Lösung

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

Lösung

- \frac{8 x}{( x ^{2} - 4 ) ^{2}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{2 x ( x ^{2} - 4 ) - 2 x x ^{2}}{( x ^{2} - 4 ) ^{2}} : - \frac{8 x}{( x ^{2} - 4 ) ^{2}}

= - \frac{8 x}{( x ^{2} - 4 ) ^{2}}

Graph

Beliebte Beispiele

derivative of 2/(sqrt(x^2-3))

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

(dy}{dx}=\frac{(y^2-1))/x

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

derivative y=34(3p+1)-2/5 ,p>0

d er i v a t i v e y = 34 (3 p + 1) - \frac{2}{5}, p > 0

(x + 1)^{^{'}}

integral of (2x-4+8sqrt(x))/(sqrt(x))

\int \frac{2 x - 4 + 8 x}{x} d x