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

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

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

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

y + z^{3}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= y + z^{3}

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