What is (\partial)/(\partial x)(2xy^3+2xy-4) ?

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

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(\partial)/(\partial x)(2xy^3+2xy-4)

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

2 y^{3} + 2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (4) = 0

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

Simplify

= 2 y^{3} + 2 y

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