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

Lösung

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

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

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

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

Vereinfache

\frac{1 \cdot ( x ^{2} - 4 ) - 2 x ( x - 2 )}{( x ^{2} - 4 ) ^{2}} : - \frac{1}{( x + 2 ) ^{2}}

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

t an g e n t y = x^{2} + x + 9, at x = 2

\frac{d}{d x} ((\frac{x ^{2} + 2}{x ^{2} - 2})^{8})

s l o p e (- 4, 2), (4, - 2)

t an g e n t f (x) = \frac{x ^{3}}{2}, at x = - 6

\int \frac{sin ( 2 x )}{1} d x