What is (\partial)/(\partial y)(e^{xyz}) ?

The answer to (\partial)/(\partial y)(e^{xyz}) is e^{xyz}xz

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(\partial)/(\partial y)(e^{xyz})

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

e^{x yz} x z

Solution steps

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

Treat

x, z

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x yz) = x z

= e^{x yz} x z

What is (\partial)/(\partial y)(e^{xyz}) ?
The answer to (\partial)/(\partial y)(e^{xyz}) is e^{xyz}xz