(\partial)/(\partial y)((x-y)/(xy+2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

s l o p e f (5) = 4 x^{2} + 3 x - \frac{8}{x ^{2}}

n = 1 \sum \infty \frac{n}{n ^{2} + 1} x^{n}

t an g e n t y = x^{2} - 2, (- 2, 2)

in v erse l a pl a ce \frac{s ^{2} + 4}{s ^{2} + 4 s + 8}

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