I'm trying to show that delta f(x) = sum_i frac delta(x-a_i) left| fracdfdx(a_i) right|? Where a_i are the roots of the function f(x). I've tried to proceed by using a dummy function g(x) and carrying out int_- infty^ inftydx , delta f(x)g(x). Then making the coordinate substitution u = f(x) and integrating over u. This seems to be on the right track, but I'm unsure where the absolute value comes in in the denominator, and also why it becomes a sum. int_- infty^ infty fracdu fracdfdx delta(u)g f⁻¹(u) = fracg f⁻¹(0) fracdfdx f⁻¹(0). Can anyone shed some light?