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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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}

Simplify

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

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

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