matrix derivative of $X^{1/2}C(X^{1/2})'$ with respect to $X$?

Question

Where $X$ and $C$ are both symmetric positive-definite matrices, and $X^{1/2}$ is the lower-triangular matrix sqare root of $X$. In other words, if $Y=X^{1/2}C{X^{1/2}}'$, what is the effect of a change in the elements of $X$ on those of $Y$? Thanks!!!