What is (\partial)/(\partial x)(xye^{yz}) ?

The answer to (\partial)/(\partial x)(xye^{yz}) is e^{yz}y

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(\partial)/(\partial x)(xye^{yz})

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

e^{yz} y

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= y e^{yz} \cdot 1

Simplify

= e^{yz} y

What is (\partial)/(\partial x)(xye^{yz}) ?
The answer to (\partial)/(\partial x)(xye^{yz}) is e^{yz}y