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

Lösung

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

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

Schritte zur Lösung

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

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

\frac{d}{d x} (2 x + 1) = 2

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

Multipliziere aus

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

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

in v erse l a pl a ce \frac{s}{9 s + 81}

\int_{0}^{π} sin (x) cos (x) d x

x \to 0 lim (\frac{1}{x} \cdot sin (\frac{1}{x}))

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

\int t cos (t) d t