(\partial)/(\partial y)((e^y)/(e^x+e^y))

Lösung

\frac{\partial}{\partial y} (\frac{e ^{y}}{e ^{x} + e ^{y}})

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

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{e ^{y}}{e ^{x} + e ^{y}})

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

\frac{\partial}{\partial y} (e^{y}) = e^{y}

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

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

Vereinfache

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

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

\frac{d}{d x} (3 x^{2} - 2 x + 5)

\int (x y e^{x z}) d z

\int x I n x d x

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

d er i v a t i v e \frac{3 w ^{6} - w}{w}