Backward Propagation and Hinge Loss

Hi

I plan to write a function which will output the derivative of a hinge loss w.r.t the ground truth. I consider the function as following from this link:

+

where as Y(the first parameter)is the prediction and Y.(the second parameter) is the ground truth.

During calcualting bakward loss, what I understand is, I need to calcualte the derivative of the above loss w.r.t the second paramter, right? In that case, will the code be like following:

function dLdX = backwardLoss1( this, Y, T )
            % backwardLoss    Back propagate the derivative of the loss
            % function
            %
            % Syntax:
            %   dLdX = layer.backwardLoss( Y, T );
            %
            % Image Inputs:
            %   Y   Predictions made by network, 1-by-1-by-numClasses-by-numObs
            %   T   Targets (actual values), 1-by-1-by-numClasses-by-numObs
            %
            % Vector Inputs:
            %   Y   Predictions made by network,  numClasses-by-numObs-by-seqLength
            %   T   Targets (actual values),  numClasses-by-numObs-by-seqLength
          if(Y*T<1)
                dLdX=-T/size(Y);
           else
                dLdX=0;
            end         
        end

But following this link, it's diplaying the calculation of the derivative w.r.t the parameters which makes me confuse that shuld I need to output the los w.rt the weights as well as w.r.t to the ground truth?

I am looking for your suggestions in this reagrd.

thanks,