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

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

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

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

x^{2} e^{yz} z

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (yz) = z

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

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