\(\frac{dU\left(x_{\left(i\right)}\right)}{dx_{\left(i\right)}}=w_i\)
Thus the net effect of the change from  \(w_i\) to \(w_i^1\)  on  \(U\left(x_i\right)\) will be \(\left(w_i^1-w_i\right).u_i\) if all other weights could be kept constant. But this clearly not the case.

Next Steps

This is an ok assignment.