What is (\partial)/(\partial z)(e^{yz}) ?

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

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(\partial)/(\partial z)(e^{yz})

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

e^{yz} y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{yz} y

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