What is (\partial)/(\partial y)(3ze^{xyz}) ?

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

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(\partial)/(\partial y)(3ze^{xyz})

\frac{\partial}{\partial y} (3 z e^{x yz})

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

Solution steps

\frac{\partial}{\partial y} (3 z e^{x yz})

Treat

z, x

as constants

Take the constant out:

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

= 3 z \frac{\partial}{\partial y} (e^{x yz})

Apply the chain rule:

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

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

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

= 3 z e^{x yz} z x

Simplify

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

= 3 e^{z x y} z^{2} x

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