Given the marginal rate of substitution of $x$ for $y$ : $\frac{u'(x)}{u'(y)} $
I know one can interpret this as the amount of $y$ one is willing to give up for an additional unit of $x$, or the amount of $y$ that has to be given to compensate the consumer for a loss of $x$.
But mathematically, is it saying, how much the consumer values the next unit of $x$, in terms of the next unit of $y$? or the marginal valuation of $x$ in terms of additional units of $y$?