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

The answer to (\partial)/(\partial x)(2x^3y^2+2y+4x) is 6x^2y^2+4

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

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

6 x^{2} y^{2} + 4

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{3} y^{2}) = 6 y^{2} x^{2}

\frac{\partial}{\partial x} (2 y) = 0

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

= 6 y^{2} x^{2} + 0 + 4

Simplify

= 6 x^{2} y^{2} + 4

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What is (\partial)/(\partial x)(2x^3y^2+2y+4x) ?
The answer to (\partial)/(\partial x)(2x^3y^2+2y+4x) is 6x^2y^2+4