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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((x - y)^{2}) = 2 (x - y) (1 - \frac{d y}{d x})

= \frac{2 x ( x - y ) ^{2} - 2 ( x - y ) ( 1 - \frac{d y}{d x} ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}}

Vereinfache

\frac{2 x ( x - y ) ^{2} - 2 ( x - y ) ( 1 - \frac{d y}{d x} ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}} : \frac{2 x ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

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

x \to 9 lim (\frac{( x + 2 )}{2})

x y d x + 3 e^{x} d y = 0

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

t a y l or \frac{1}{( 1 + 4 x )}

\frac{\partial}{\partial x} (cos (y^{2}) + y e^{x})