3. Evaluate the following mixted partial derivatives
(1) $f(r,s,t) = r \ln(rs^2t^3)$ $f_{rss}$, $f_{rst}$;
(2) $f(x, y, z) = \cos(4x+3y+2z)$; $f_{xyz}$, $f_{yzz}$;
(3) $u = e^{r\theta} \sin\theta$ $u_{rr\theta}$
4. If $f = xe^y + ye^x$, show that
$f_{xxx} + f_{yyy} = xf_{xyy} + yf_{xxy}$