#14.6 #8 <<USE THE CHAIN RULE>> to find the partials of z with
respect to u and v if
z = cos(x^2+y^2); x = u cos(v); y = u sin(v)



Answer:
z_u = z_x x_u + z_y y_u
    = -2x sin(x^2+y^2) cos(v) - 2y sin(x^2+y^2) sin(v)

z_v = z_x x_v + z_y y_v
    = +2x sin(x^2+y^2) u sin(v) - 2y sin(x^2+y^2) u cos(v)


If the problem hadn't say to use the chain rule, one could have 
done things like x^2+y^2 = u^2 so z = cos(u^2) and hence
z_u = -2u sin(u^2) and z_v = 0. But this would be the wrong
method, for this problem.