What is (\partial)/(\partial x)((z)(-e^z+2xyz)) ?

The answer to (\partial)/(\partial x)((z)(-e^z+2xyz)) is 2z^2y

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(\partial)/(\partial x)((z)(-e^z+2xyz))

\frac{\partial}{\partial x} ((z) (- e^{z} + 2 x yz))

2 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (- e^{z} + 2 x yz))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (- e^{z} + 2 x yz)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (- \frac{\partial}{\partial x} (e^{z}) + \frac{\partial}{\partial x} (2 x yz))

\frac{\partial}{\partial x} (e^{z}) = 0

\frac{\partial}{\partial x} (2 x yz) = 2 zy

= z (- 0 + 2 zy)

Simplify

z (- 0 + 2 zy) : 2 z^{2} y

= 2 z^{2} y

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What is (\partial)/(\partial x)((z)(-e^z+2xyz)) ?
The answer to (\partial)/(\partial x)((z)(-e^z+2xyz)) is 2z^2y