derivative (1-5x-x^2)/(x^2-3)

Lösung

ableitung von

\frac{1 - 5 x - x ^{2}}{x ^{2} - 3}

\frac{5 x ^{2} + 4 x + 15}{( x ^{2} - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 - 5 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 - 5 x - x ^{2} ) ( x ^{2} - 3 ) - \frac{d}{d x} ( x ^{2} - 3 ) ( 1 - 5 x - x ^{2} )}{( x ^{2} - 3 ) ^{2}}

\frac{d}{d x} (1 - 5 x - x^{2}) = - 2 x - 5

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

= \frac{( - 2 x - 5 ) ( x ^{2} - 3 ) - 2 x ( 1 - 5 x - x ^{2} )}{( x ^{2} - 3 ) ^{2}}

Multipliziere aus

(- 2 x - 5) (x^{2} - 3) - 2 x (1 - 5 x - x^{2}) : 5 x^{2} + 4 x + 15

= \frac{5 x ^{2} + 4 x + 15}{( x ^{2} - 3 ) ^{2}}

(e^{2 x} + 4) y^{^{'}} = y

\int (2 x + 1)^{5} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x^{2} - 5

\frac{d y}{d x} = \frac{y ^{2}}{e ^{x}}

d er i v a t i v e y = 1 4^{- \frac{8}{x}}