What is (\partial)/(\partial z)(xe^y+ye^z+ze^x) ?

The answer to (\partial)/(\partial z)(xe^y+ye^z+ze^x) is e^zy+e^x

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(\partial)/(\partial z)(xe^y+ye^z+ze^x)

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

e^{z} y + e^{x}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial z} (x e^{y}) = 0

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

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

= 0 + y e^{z} + e^{x}

Simplify

= e^{z} y + e^{x}

What is (\partial)/(\partial z)(xe^y+ye^z+ze^x) ?
The answer to (\partial)/(\partial z)(xe^y+ye^z+ze^x) is e^zy+e^x