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

Lösung

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

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

Schritte zur Lösung

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

Behandle

c, x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

= c \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

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

Vereinfache

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

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

x \to 2 lim (\frac{1}{x - 1})

\int 3 + x d x

x \to + 1 + lim (x)

x \to 9 lim (\frac{5}{x + 5})

n = 0 \sum \infty (x - 3)^{n}