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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e cos (x sin (x))

\frac{d}{d x} (\frac{- 6 x}{1 - x})

in v erse l a pl a ce \frac{s + 4}{s ^{2} + 6 s + 18}

\int a x^{5} d x

a re a y = x^{2}, y = 8 - x^{2}, y = 4 x + 11