derivative f(x)= x/(x^2-6)

Lösung

ableitung von

f (x) = \frac{x}{x ^{2} - 6}

\frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - 6})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) x}{( x ^{2} - 6 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 6) = 2 x

= \frac{1 \cdot ( x ^{2} - 6 ) - 2 xx}{( x ^{2} - 6 ) ^{2}}

1 \cdot (x^{2} - 6) - 2 xx = - x^{2} - 6

= \frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}}

\int_{- 3}^{0} - x^{2} - 3 x d x

\int coth (x) d x

\int \frac{t}{t ^{3}} d t

x \to 0 lim (\frac{x}{1 - cos ( x )})

\frac{d}{d x} ((2 cos (2 x) + sin (3 x) + 3)^{2})