derivative of (8x^3-6x^2/(x^2+3x-2))

Lösung

\frac{d}{d x} (\frac{8 x ^{3} - 6 x ^{2}}{x ^{2} + 3 x - 2})

\frac{8 x ^{4} + 48 x ^{3} - 66 x ^{2} + 24 x}{( x ^{2} + 3 x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{3} - 6 x ^{2}}{x ^{2} + 3 x - 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x ^{3} - 6 x ^{2} ) ( x ^{2} + 3 x - 2 ) - \frac{d}{d x} ( x ^{2} + 3 x - 2 ) ( 8 x ^{3} - 6 x ^{2} )}{( x ^{2} + 3 x - 2 ) ^{2}}

\frac{d}{d x} (8 x^{3} - 6 x^{2}) = 24 x^{2} - 12 x

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

= \frac{( 24 x ^{2} - 12 x ) ( x ^{2} + 3 x - 2 ) - ( 2 x + 3 ) ( 8 x ^{3} - 6 x ^{2} )}{( x ^{2} + 3 x - 2 ) ^{2}}

Multipliziere aus

(24 x^{2} - 12 x) (x^{2} + 3 x - 2) - (2 x + 3) (8 x^{3} - 6 x^{2}) : 8 x^{4} + 48 x^{3} - 66 x^{2} + 24 x

= \frac{8 x ^{4} + 48 x ^{3} - 66 x ^{2} + 24 x}{( x ^{2} + 3 x - 2 ) ^{2}}

\int_{2}^{4} \frac{1}{16 - t ^{2}} d t

x \to 2 lim (2 x - 2)

\int \frac{sec ( x )}{x} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = - 3 t e^{- t}

\int x^{2} sin (4 x) d x