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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (e^{c o s (x)} \cdot sin (x^{2} - x))

a re a 2 x^{2}, 2 x + 6, - 1.3, 2.3

in v erse l a pl a ce \frac{s}{s ^{2} + 10 s + 25}

x \to 0 lim (\frac{5}{x} - \frac{5}{x ^{2} + x})

t \to 1 lim (t + 3)