derivative of (x^2-4/(x^2-1))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 1})

\frac{6 x}{( x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 4}{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} - 4 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( x ^{2} - 4 )}{( x ^{2} - 1 ) ^{2}}

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

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

= \frac{2 x ( x ^{2} - 1 ) - 2 x ( x ^{2} - 4 )}{( x ^{2} - 1 ) ^{2}}

Multipliziere aus

2 x (x^{2} - 1) - 2 x (x^{2} - 4) : 6 x

= \frac{6 x}{( x ^{2} - 1 ) ^{2}}

\frac{\partial}{\partial y} (7 x^{7} y^{4} + 2 x^{8} y^{6})

\int_{0}^{9} 6 - 2 x d x

\int \frac{x}{25 + 16 x ^{4}} d x

\int \frac{x ^{2}}{6 - x} d x

x \to 2 lim (f (x))