When comparing with the network output with desired output, if there is error the weight vector w(k) associated with the ith processing unit at the time instant k is corrected (adjusted) as
w(k+1) = w(k) + D[w(k)]
where, D[w(k)] is the change in the weight vector and will be explicitly given for various learning rules.
Delta Learning rule is given by:
w(k+1) = w(k) + eta*[ d(k) - f{ w'(k)*x(k) } ] *f'{ w'(k)*x(k) } *x(k)

Widrow-Hoff Learning rule is given by:

w(k+1) = w(k) + eta*[ d(k) - w'(k)*x(k) ] *x(k)
here: f{ w'(k)*x(k) } = w'(k)*x(k)

Reference:
http://www.ent.mrt.ac.lk/~ekulasek/ami/PartC.pdf