What is (\partial)/(\partial x)(y^2e^{xyz}) ?

The answer to (\partial)/(\partial x)(y^2e^{xyz}) is e^{yxz}y^3z

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(\partial)/(\partial x)(y^2e^{xyz})

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

e^{y x z} y^{3} z

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

y^{2} e^{x yz} yz : e^{y x z} y^{3} z

= e^{y x z} y^{3} z

What is (\partial)/(\partial x)(y^2e^{xyz}) ?
The answer to (\partial)/(\partial x)(y^2e^{xyz}) is e^{yxz}y^3z