ionship between $f_{xy}$
      and $f_{yx}$. Then use your conjecture to quickly compute
      $f_{xy}$ if $$f(x,y)=3xy^2+\tan^{2}(\cos(x))
      (x^{49}+x)^{1000}.$$</li>
    </ol>
  </div><a href= "http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Clairaut.27s_theorem">Clairaut's
  theorem</a> implies that if a function $f$ is
  &ldquo;nice&rdquo;&mdash;if $f$ and its partial derivatives and
  second partials are defined and continuous around a point
  $(a,b)$, then $f_{xy}=f_{yx}$ at that point