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

Lösung

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

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

Schritte zur Lösung

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

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

\frac{\partial}{\partial y} (x + y) = 1

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

Vereinfache

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

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

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

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

\int_{2}^{5} \frac{1}{x + 1} d x

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

\int \frac{81 - x ^{2}}{x ^{2}} d x