What is (\partial)/(\partial z)(xe^{y/z}) ?

The answer to (\partial)/(\partial z)(xe^{y/z}) is -(e^{y/z}xy)/(z^2)

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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}})

Simplify

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))

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

\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)

What is (\partial)/(\partial z)(xe^{y/z}) ?
The answer to (\partial)/(\partial z)(xe^{y/z}) is -(e^{y/z}xy)/(z^2)