dx/du = ln v
dx/dv = u/v
dy/du = v/u
dy/dv = ln u
dz/dx = y^2(-sin x) = -y^2 sin x
dz/dy = 2y cos x
dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)
dz/du = -y^2 sin x*ln v + 2y cos x*v/u
dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*dy/dv
dz/dv = -y^2 sin x*u/v + 2y cos x*ln u