derivative (1-3x-x^2)/(x^2-3)

Lösung

ableitung von

\frac{1 - 3 x - x ^{2}}{x ^{2} - 3}

\frac{3 x ^{2} + 4 x + 9}{( x ^{2} - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 - 3 x - x ^{2}}{x ^{2} - 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 1 - 3 x - x ^{2} ) ( x ^{2} - 3 ) - \frac{d}{d x} ( x ^{2} - 3 ) ( 1 - 3 x - x ^{2} )}{( x ^{2} - 3 ) ^{2}}

\frac{d}{d x} (1 - 3 x - x^{2}) = - 2 x - 3

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

= \frac{( - 2 x - 3 ) ( x ^{2} - 3 ) - 2 x ( 1 - 3 x - x ^{2} )}{( x ^{2} - 3 ) ^{2}}

Multipliziere aus

(- 2 x - 3) (x^{2} - 3) - 2 x (1 - 3 x - x^{2}) : 3 x^{2} + 4 x + 9

= \frac{3 x ^{2} + 4 x + 9}{( x ^{2} - 3 ) ^{2}}

l a pl a ce t r an s f or m 2 t^{3}

\frac{d}{d x} (sin (x) ln (x^{2} + 1))

im pl i c i t \frac{d y}{d x}, tan (x - y) = \frac{y}{1 - x ^{2}}

\int cot (42 x) d x

\frac{d}{d x} (3^{x^{3} - x + 1})