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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial y} (x) = 0

= - \frac{2 x y}{( x ^{2} + y ^{2} ) ^{2}} + 0

Vereinfache

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

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

\int e^{x} \cdot cos (x) d x

x \to 0 + lim (x^{2} + 5)

\int_{0}^{\frac{π}{6}} 8 sec^{3} (x) d x

a re a \frac{2}{x}, 8 x, \frac{x}{8}