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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

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

\frac{d}{d z} (z^{2})

\int x^{3} a x^{4} + b d x

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

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

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