derivative of (4-2x-x^2/(x^2-6))

Lösung

\frac{d}{d x} (\frac{4 - 2 x - x ^{2}}{x ^{2} - 6})

\frac{2 x ^{2} + 4 x + 12}{( x ^{2} - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 - 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} ( 4 - 2 x - x ^{2} ) ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) ( 4 - 2 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

\frac{d}{d x} (4 - 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 ( 4 - 2 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

Multipliziere aus

(- 2 x - 2) (x^{2} - 6) - 2 x (4 - 2 x - x^{2}) : 2 x^{2} + 4 x + 12

= \frac{2 x ^{2} + 4 x + 12}{( x ^{2} - 6 ) ^{2}}

x v^{'} + v = \frac{( 1 + 2 v )}{1 - v}

d er i v a t i v e x^{4} ln (x)

4 y^{^{''}} - 8 y^{^{'}} + 7 y = 0

y^{^{''}} + 64 y = sec^{2} (8 x)

\int cos (4 x + 1) d x