derivative of (3-2x-x^2/(x^2-6))

Lösung

\frac{d}{d x} (\frac{3 - 2 x - x ^{2}}{x ^{2} - 6})

\frac{2 x ^{2} + 6 x + 12}{( x ^{2} - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 - 2 x - x ^{2}}{x ^{2} - 6})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 - 2 x - x ^{2} ) ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) ( 3 - 2 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

\frac{d}{d x} (3 - 2 x - x^{2}) = - 2 x - 2

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

= \frac{( - 2 x - 2 ) ( x ^{2} - 6 ) - 2 x ( 3 - 2 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

Multipliziere aus

(- 2 x - 2) (x^{2} - 6) - 2 x (3 - 2 x - x^{2}) : 2 x^{2} + 6 x + 12

= \frac{2 x ^{2} + 6 x + 12}{( x ^{2} - 6 ) ^{2}}

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

\int 5^{2 x} d x

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

\int (x^{2} - 2 x + 4) d x

(2 x^{2} - y e^{x}) d x - e^{x} d y = 0