derivative of (x^3/(4-x^2))

Lösung

\frac{d}{d x} (\frac{x ^{3}}{4 - x ^{2}})

\frac{12 x ^{2} - x ^{4}}{( 4 - x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3}}{4 - x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{3} ) ( 4 - x ^{2} ) - \frac{d}{d x} ( 4 - x ^{2} ) x ^{3}}{( 4 - x ^{2} ) ^{2}}

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

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

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

Vereinfache

\frac{3 x ^{2} ( 4 - x ^{2} ) - ( - 2 x ) x ^{3}}{( 4 - x ^{2} ) ^{2}} : \frac{12 x ^{2} - x ^{4}}{( 4 - x ^{2} ) ^{2}}

= \frac{12 x ^{2} - x ^{4}}{( 4 - x ^{2} ) ^{2}}

\int 5 sin (3 x) sin (6 x) d x

in v erse l a pl a ce \frac{15}{3 s + 3}

\frac{d y}{d t} + 0.7 t y = 7 t, y (0) = 7

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 x)

\int \frac{8}{4 - x ^{2}} d x