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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

(\partial)/(\partial x)(sqrt(4-x^2-4Y(x)^2))

\frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x)^{2})

derivative of-x^3+5x^2-6x

\frac{d}{d x} (- x^{3} + 5 x^{2} - 6 x)

integral of ((x^2))/(1+x^2)

\int \frac{( x ^{2} )}{1 + x ^{2}} d x

derivative y= 4/(5-3(x))

d er i v a t i v e y = \frac{4}{5 - 3 ( x )}

limit as x approaches 4 of x/(x-4)

x \to 4 lim (\frac{x}{x - 4})