What is (\partial)/(\partial z)(xy+z^3x-2yz) ?

The answer to (\partial)/(\partial z)(xy+z^3x-2yz) is 3xz^2-2y

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(\partial)/(\partial z)(xy+z^3x-2yz)

\frac{\partial}{\partial z} (x y + z^{3} x - 2 yz)

3 x z^{2} - 2 y

Solution steps

\frac{\partial}{\partial z} (x y + z^{3} x - 2 yz)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x y) + \frac{\partial}{\partial z} (z^{3} x) - \frac{\partial}{\partial z} (2 yz)

\frac{\partial}{\partial z} (x y) = 0

\frac{\partial}{\partial z} (z^{3} x) = 3 x z^{2}

\frac{\partial}{\partial z} (2 yz) = 2 y

= 0 + 3 x z^{2} - 2 y

Simplify

= 3 x z^{2} - 2 y

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What is (\partial)/(\partial z)(xy+z^3x-2yz) ?
The answer to (\partial)/(\partial z)(xy+z^3x-2yz) is 3xz^2-2y