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

Lösung

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

\frac{11 x ^{2} - 10 x - 7}{( 2 x ^{2} + 5 x - 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 x^{2} + 5 x - 1) = 4 x + 5

= \frac{( 2 x - 3 ) ( 2 x ^{2} + 5 x - 1 ) - ( 4 x + 5 ) ( x ^{2} - 3 x + 2 )}{( 2 x ^{2} + 5 x - 1 ) ^{2}}

Multipliziere aus

(2 x - 3) (2 x^{2} + 5 x - 1) - (4 x + 5) (x^{2} - 3 x + 2) : 11 x^{2} - 10 x - 7

= \frac{11 x ^{2} - 10 x - 7}{( 2 x ^{2} + 5 x - 1 ) ^{2}}

\frac{\partial}{\partial y} (\frac{2 y}{x + y ^{2}})

\int \frac{5 ln ^{2} ( x ) + 9}{x} d x

\frac{\partial}{\partial x} (y^{2} + x y + 3 y + 2 x + 3)

\int \frac{1}{5 sin ( x ) + 3} d x

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 15 x)