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

Lösung

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

\frac{x ^{4} + 6 x ^{2}}{( x ^{2} + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3 x ^{2} ( x ^{2} + 2 ) - 2 x x ^{3}}{( x ^{2} + 2 ) ^{2}} : \frac{x ^{4} + 6 x ^{2}}{( x ^{2} + 2 ) ^{2}}

= \frac{x ^{4} + 6 x ^{2}}{( x ^{2} + 2 ) ^{2}}

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

y^{^{'}} = y (1 - 0.0002 y)

in v erse l a pl a ce \frac{1}{( s + 2 ) ( s ^{2} - 2 s + 5 )}

\int_{- 3}^{- 1} x^{2} e^{x^{3} + 27} d x

\int tan^{2} (a x) cos (a x) d x