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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ( x ^{3} + 3 x ^{2} ) - ( 3 x ^{2} + 6 x ) ( x ^{2} - 2 )}{( x ^{3} + 3 x ^{2} ) ^{2}} : - \frac{x ^{3} - 6 x - 12}{x ^{3} ( x + 3 ) ^{2}}

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

d er i v a t i v e y = \frac{x + x ^{3}}{x ^{2}}

d er i v a t i v e f (x) = 7 - 2 x

\frac{\partial}{\partial x} (2 x^{3} + 4 y - 2 z^{2})

\int 2 \cdot x \cdot ln (4 x) d x

\int y x d x