(\partial)/(\partial x)((e^{xy})/(x+y))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

\frac{d}{d x} (3 \frac{8 x ^{2} - 3}{x ^{2} + 2})

\int \frac{e ^{3}}{x} d x

x \to 0 lim (\frac{∣ x ∣}{4 x})

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 36 y = 0

\int tan (\frac{t}{2}) d t