(\partial)/(\partial y)((x^2y-y)/(x^2-2y))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( x ^{2} - 1 ) ( x ^{2} - 2 y ) - ( - 2 ) ( x ^{2} y - y )}{( x ^{2} - 2 y ) ^{2}} : \frac{x ^{4} - x ^{2}}{( x ^{2} - 2 y ) ^{2}}

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

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

y^{3} - (10 x + 8) + 3 x y^{2} y^{^{'}} = 0

d er i v a t i v e \frac{x - 4}{x + 4}

d er i v a t i v e y = \frac{1}{3 x}

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