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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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