derivative x/(x^2-8)

Lösung

ableitung von

\frac{x}{x ^{2} - 8}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

= \frac{1 \cdot ( x ^{2} - 8 ) - 2 xx}{( x ^{2} - 8 ) ^{2}}

1 \cdot (x^{2} - 8) - 2 xx = - x^{2} - 8

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

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

x \to \infty lim (4^{x} - 1)

x \to 3 lim (\frac{( x ^{2} - 9 )}{2 x - 6})

x \to \infty lim (\frac{2 ^{x}}{3 ^{x - 1}})

\int 2 - x d x