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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (\frac{y}{z}) = \frac{1}{z}

= x e^{\frac{y}{z}} \frac{1}{z}

Vereinfache

x e^{\frac{y}{z}} \frac{1}{z} : \frac{e ^{\frac{y}{z}} x}{z}

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

\frac{d}{d x} (\frac{3}{2 - x})

x \to 0 lim (2 + 3 e^{- \frac{3}{x}})

\frac{d}{d x} (2 sin (\frac{1}{2} x))

\int - 2 x d x

d er i v a t i v e y = e^{x^{2} + 9 x + 4}