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

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

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(\partial)/(\partial z)(e^{-xyz})

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

- e^{- x yz} x y

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

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

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

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

= e^{- x yz} (- x y)

Simplify

= - e^{- x yz} x y

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