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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

1 \cdot (x^{2} - 1) - 2 xx = - x^{2} - 1

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

\frac{\partial}{\partial y} (ln (\frac{x}{x ^{2} + y ^{2}}))

\int x 4^{x} d x

d er i v a t i v e y = (cos (x))^{s i n (x)}

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

x \to 2 lim ((3 - x) (x + 1))