title: Compute partial derivatives with `madness`
body: <p>The <code>madness</code> packages, as mentioned <a href="https://stackoverflow.com/questions/69876390/using-deriv-package-for-derivative-wrt-vector/69876456?noredirect=1#comment123519149_69876456">here</a>, is nice for autodiff in R.</p>
  <p>I would like to compute now a derivative wrt x of a derivative wrt y.</p>
  <p>$\frac{\partial}{\partial x}\frac{\partial}{\partial y}xy$</p>
  <p><img src="https://chart.googleapis.com/chart?cht=tx&amp;chl=%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7Dxy" alt="" /></p>
  <p>how can this be done using <code>madness</code>?</p>
  <p>update: actually here I guess it factors.. maybe this will be ok by just multiplying the two derivatives?  Maybe this will only be difficult if x is a function of y.</p>