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

Lösung

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

\frac{9 x ^{2} - x ^{4}}{( 3 - x ^{2} ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{3 x ^{2} ( 3 - x ^{2} ) - ( - 2 x ) x ^{3}}{( 3 - x ^{2} ) ^{2}} : \frac{9 x ^{2} - x ^{4}}{( 3 - x ^{2} ) ^{2}}

= \frac{9 x ^{2} - x ^{4}}{( 3 - x ^{2} ) ^{2}}

d er i v a t i v e \frac{1}{2 x + 10}

y^{^{'}} = 2 x e^{y}

\frac{\partial}{\partial x} (e^{x y} cos (b x + c))

\frac{d y}{d x} = 2 + y - 2 x + 4

im pl i c i t \frac{d y}{d x}, 2 x y = 6