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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

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}}

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

Vereinfache

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

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

\int_{25}^{50} 20 d x

d er i v a t i v e f (x) = \frac{x ^{2} + 1}{x + 4}

d er i v a t i v e f (x) = x^{\frac{5}{2}} (2 - 5 x^{3})

l a pl a ce t r an s f or m e^{(- 2 x)} (3 x)^{2}

t an g e n t f (x) = - 5 sin (x), at x = \frac{π}{4}