What is (\partial)/(\partial z)(x^2+y^2z) ?

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

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(\partial)/(\partial z)(x^2+y^2z)

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

y^{2}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial z} (x^{2}) = 0

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

= 0 + y^{2}

Simplify

= y^{2}

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