What is (\partial)/(\partial x)(7-e^{xyz}) ?

The answer to (\partial)/(\partial x)(7-e^{xyz}) is -e^{xyz}yz

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(\partial)/(\partial x)(7-e^{xyz})

\frac{\partial}{\partial x} (7 - e^{x yz})

- e^{x yz} yz

Solution steps

\frac{\partial}{\partial x} (7 - e^{x yz})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (7) - \frac{\partial}{\partial x} (e^{x yz})

\frac{\partial}{\partial x} (7) = 0

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

= 0 - e^{x yz} yz

Simplify

= - e^{x yz} yz

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What is (\partial)/(\partial x)(7-e^{xyz}) ?
The answer to (\partial)/(\partial x)(7-e^{xyz}) is -e^{xyz}yz