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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

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