derivative x/(x^2-9)

Lösung

ableitung von

\frac{x}{x ^{2} - 9}

\frac{- x ^{2} - 9}{( x ^{2} - 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} - 9 ) - \frac{d}{d x} ( x ^{2} - 9 ) x}{( x ^{2} - 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 9) = 2 x

= \frac{1 \cdot ( x ^{2} - 9 ) - 2 xx}{( x ^{2} - 9 ) ^{2}}

1 \cdot (x^{2} - 9) - 2 xx = - x^{2} - 9

= \frac{- x ^{2} - 9}{( x ^{2} - 9 ) ^{2}}

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

d er i v a t i v e 2 sin (t) \cdot cos (t)

y^{^{'}} = (x + y - 4)^{2}

x \to 1 lim (cos (π \cdot x))

\int_{2}^{\infty} x e^{- x^{2}} d x