The 8th step of the calculation is wrong, which does not gives the same result as step 9 after simplification by miscalculating the partial differentiation of y(xi) from step 7. Please ignore or delete step 8 for consistency of the answer.

The detailed calculation is below, the black notes shows the steps of calculation from the beginning and the blue notes shows the inverse calculation from step 9 to step 8 to prove the correction.
