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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\int \frac{x}{x ^{2} + 6} d x

t an g e n t f (x) = 9 x^{2} - x^{3}, (2, 28)

\frac{d}{d x} (\frac{1}{3 x ^{5}})

d er i v a t i v e f (x) = (\frac{sin ( x )}{x})^{2}