What is (\partial)/(\partial x)(yze^{xz}+40) ?

The answer to (\partial)/(\partial x)(yze^{xz}+40) is e^{zx}yz^2

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(\partial)/(\partial x)(yze^{xz}+40)

\frac{\partial}{\partial x} (yz e^{x z} + 40)

e^{z x} y z^{2}

Solution steps

\frac{\partial}{\partial x} (yz e^{x z} + 40)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (yz e^{x z}) + \frac{\partial}{\partial x} (40)

\frac{\partial}{\partial x} (yz e^{x z}) = y z^{2} e^{z x}

\frac{\partial}{\partial x} (40) = 0

= y z^{2} e^{z x} + 0

Simplify

= e^{z x} y z^{2}

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What is (\partial)/(\partial x)(yze^{xz}+40) ?
The answer to (\partial)/(\partial x)(yze^{xz}+40) is e^{zx}yz^2