What is (\partial)/(\partial x)(xy^2z^3+3yz) ?

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

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(\partial)/(\partial x)(xy^2z^3+3yz)

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

y^{2} z^{3}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 yz) = 0

= y^{2} z^{3} + 0

Simplify

= y^{2} z^{3}

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