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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x z) = z

= yz e^{x z} z

Simplify

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

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

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