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

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

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

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

4 x y - 2

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (4 y^{3}) = 0

= 4 y x - 2 + 0

Simplify

= 4 x y - 2

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