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

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

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

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

3 x^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 3 x^{2}

Simplify

= 3 x^{2}

3 x^{2} cos (3 x)

\frac{\partial}{\partial x} (5 x y - 3 x^{2} y)

\int x^{4} cos (x^{5}) d x

x \to 2 lim (\frac{2}{x} + 4)

\int_{0}^{4} \frac{2}{x} d x

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