question about the jacobian of pmsm2d in elmer

[lij30403]

For pmsm, I computed the Jacobian differently, can you guys explain whether Im wrong:
M(x) = nu * stiff
f(x) = M(x)x -b
d/dx (f(x)) = M(x) + d/dx(M(x))x-b
=M(x) + muder/babs * diag(int (B_i \dot \nabla \phi_i) * (\sum_k B_k \dot \nabla \phi_i)dx)
rather than the jacobian for pmsm in elmer:
M(x)+muder/babs (\int (B_i \dot \nabla \phi_i) * (B_j \dot \nabla \phi_j))_{ij}

can you explain me this?