What is (\partial)/(\partial z)(x^2y^4+z^3) ?

The answer to (\partial)/(\partial z)(x^2y^4+z^3) is 3z^2

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(\partial)/(\partial z)(x^2y^4+z^3)

\frac{\partial}{\partial z} (x^{2} y^{4} + z^{3})

3 z^{2}

Solution steps

\frac{\partial}{\partial z} (x^{2} y^{4} + z^{3})

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x^{2} y^{4}) + \frac{\partial}{\partial z} (z^{3})

\frac{\partial}{\partial z} (x^{2} y^{4}) = 0

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

= 0 + 3 z^{2}

Simplify

= 3 z^{2}

What is (\partial)/(\partial z)(x^2y^4+z^3) ?
The answer to (\partial)/(\partial z)(x^2y^4+z^3) is 3z^2