Question

frist derivative of fermi dirac distribution with respect to energy is
dirac delta function,
step function,
gauss function
,lorenz function​

Answer 1

Dirac Delta function is zero everywhere except for a specific point where it raises to infinity. For simplicity I have taken that point as origin. (-∞,0) U (0,∞) . So in this region the differentiation of Dirac Delta function in this region is zero whereas it is not differentiable at origin.