What is (\partial)/(\partial x)(x^2y^3+4xyz-3yz) ?

The answer to (\partial)/(\partial x)(x^2y^3+4xyz-3yz) is 2xy^3+4yz

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(\partial)/(\partial x)(x^2y^3+4xyz-3yz)

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

2 x y^{3} + 4 yz

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 x yz) = 4 yz

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

= 2 y^{3} x + 4 yz - 0

Simplify

= 2 x y^{3} + 4 yz

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What is (\partial)/(\partial x)(x^2y^3+4xyz-3yz) ?
The answer to (\partial)/(\partial x)(x^2y^3+4xyz-3yz) is 2xy^3+4yz