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Homework Statement
[itex]x^{3}y + y^{3}x = 30[/itex]
Homework Equations

The Attempt at a Solution
My understanding is that I'm supposed to take the derivative of each side and try to solve for y'.
But, I don't know how to treat the y when I am differentiating it, to a power or whatever.
For example, here I did
[itex]Dx(x^{3}y) + Dx(y^{3}x) = Dx(30)[/itex]
When differentiating the first term, using the product rule, I have to get Dx(y). Simply saying that it's 1 doesn't seem to work, so I just leave it as y'. Using the product rule on that first term on the left side gives me:
y' + 3(x^2)y.
Added to the derivative of (y^3)(x). But that's the derivative I'm having trouble with.
Can anyone walk me through this? How do I treat y when differentiating a term with it in it? I don't understand.