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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int (x + 2) (x - 3) d x

\int_{0}^{1} t 4 + 9 t^{2} d t

\int e^{-}

\frac{d}{d x} (\frac{1}{2 π} e^{\frac{- x ^{2}}{2}})

x \to 3 lim (\frac{x - 3}{x + 3})