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

Lösung

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

- \frac{e ^{\frac{x}{y}} x}{y ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{e ^{\frac{x}{y}} x}{y ^{2}}

\frac{d}{d x} (7^{9 x})

\int x^{3} \cdot x^{2} + 1 d x

d er i v a t i v e x^{3} - 8 x^{2} + 5 x + 8

in v erse l a pl a ce \frac{1}{2 s ^{2}}

\frac{d y}{d x} + x y = e^{x} y