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}

\int \frac{x}{x ^{4} - 16} d x

\int sin (3 x) d x

\int_{0}^{5} 25 - x^{2} d x

h \to 0 lim (x^{2} + 2 x + h - 4)

x \to 0 lim (x^{2})

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