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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

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

Vereinfache

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

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

d er i v a t i v e cos (6 y)

\frac{d}{d x} (\frac{a x + b}{c x + d})

x \to 1 lim (arccos (x))

\frac{d}{d s} (\frac{6}{s ^{2} + 36})

\frac{d ^{2}}{d x ^{2}} (x^{2} + 16)