(\partial)/(\partial x)(1/(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2}})

Behandle

y

als Konstante

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{0}^{1} (3 x - 1)^{50} d x

\int 7 x^{9} e^{- x^{5}} d x

\frac{\partial}{\partial x} (4 e^{x} ln (1 + y))

x \to \infty + lim ((1 + \frac{1}{x})^{\frac{x}{6}})

n = 6 \sum \infty \frac{n}{n ^{2} + 1}