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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

\int sin (13 x) d x

\int_{0}^{1} ln (4 x) d x

\int - \frac{4}{x} d x

t an g e n t (x - 2) (x^{2} + 4)

d er i v a t i v e 6 cos (x)