Question: I'm checking my work here. Have I calculated these derivatives correctly in relation to the log-likelihood function below or do I need to do partial derivative with respect to j?

Log-likelihood function:

l()=i=1mlog(1+exp(Txi))+(yi1)Txi

The goal is to show the mathematical derivation of the gradient for the cost function l().

=i=1m(log(1+exp(Txi)))+(yi1)Txi

=i=1m1+exp(thetaTxi)xiexp(Txi)+yixixi

i=1mxi(yi1(1+exp(Txi)1))

Or should the final expression be:

i=1mxi,j(yi1(1+exp(Txi)1))