(\partial)/(\partial y)(sqrt((x+2)/(y+2)))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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