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

Lösung

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

- \frac{2 ( x ^{2} - y ^{2} )}{z ^{3}}

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (x^{2} - y^{2}) (- 2 z^{- 2 - 1})

Vereinfache

(x^{2} - y^{2}) (- 2 z^{- 2 - 1}) : - \frac{2 ( x ^{2} - y ^{2} )}{z ^{3}}

= - \frac{2 ( x ^{2} - y ^{2} )}{z ^{3}}

\frac{d}{d x} (\frac{( 6 - sec ( x ) )}{tan ( x )})

n = 1 \sum \infty (\frac{3}{2})^{n}

\int \frac{6 x + 4}{3 x ^{2} + 4 x + 5} d x

a re a x^{3} - 1, x = - 1, x = 2

\int_{- 10}^{10} \frac{1}{100 + x ^{2}} d x