What is (\partial)/(\partial z)(xy+z^3) ?

The answer to (\partial)/(\partial z)(xy+z^3) is 3z^2

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(\partial)/(\partial z)(xy+z^3)

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

3 z^{2}

Solution steps

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

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

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

= 0 + 3 z^{2}

Simplify

= 3 z^{2}

y = 2 sin (x), y = 2 cos (x)

3 x, x 1 8^{2} - x^{2}

\frac{\partial}{\partial y} (e^{6 x y} \cdot 6 x)

x \to 0 lim (\frac{8}{x} - \frac{8}{x ^{2} + x})

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