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

The answer to (\partial)/(\partial x)((z)(7xyz-e^z)) is 7z^2y

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(\partial)/(\partial x)((z)(7xyz-e^z))

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

7 z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (7 x yz) = 7 zy

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

= z (7 zy - 0)

Simplify

z (7 zy - 0) : 7 z^{2} y

= 7 z^{2} y

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What is (\partial)/(\partial x)((z)(7xyz-e^z)) ?
The answer to (\partial)/(\partial x)((z)(7xyz-e^z)) is 7z^2y