Discontinuity and Dirac's Delta Function 
Can someone help me understand how he came up with Dirac's function to differentiate that discontinuous periodic function? I am familiar with Dirac's function, but I don't understand where it came from in this case. Thanks

The function in the figure can be constructed by the sum of $i(t)=-t/T$ {which is a straight line at -45 degree slope through the origin} and $j(t)=\sum{} h(t-nT)$ {which is a 'staircase' function comprised of the sum of Heaviside step functions} . 
The derivative of $i(t)+j(t)$ yields your results.  So the Dirac distribution 'spikes' come from differentiating the Heaviside step functions in $j(t)$  since the derivative of $h(x-a)$ is $\delta(x-a)$ .
