derivative f(x)= x/(x^2-2)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

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

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

d er i v a t i v e 3 x \cdot y

d er i v a t i v e f (x) = 2 x^{3}

\int_{0}^{\frac{π}{4}} 5 tan^{3} (x) d x

t y^{^{'}} + 2 y = t^{2} - t + 1, y (1) = \frac{1}{2}

t an g e n t f (x) = (x^{3} + 2) (3 x^{2} - 4 x + 2), (1, 3)