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

The answer to (\partial)/(\partial y)(3x^2y^4+3) is 12x^2y^3

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

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

12 x^{2} y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (3 x^{2} y^{4}) = 12 x^{2} y^{3}

\frac{\partial}{\partial y} (3) = 0

= 12 x^{2} y^{3} + 0

Simplify

= 12 x^{2} y^{3}

What is (\partial)/(\partial y)(3x^2y^4+3) ?
The answer to (\partial)/(\partial y)(3x^2y^4+3) is 12x^2y^3