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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

t an g e n t y = 14 x sin (x), (\frac{π}{2}, 7 π)

x \to \infty lim (xx)

\int 3 cos^{3} (6 x) d x

\int cos^{10} (2 y) sin^{3} (2 y) d y

\frac{d}{d x} (\frac{1}{9} x - ln (3 x))