I have two quantities involving Dirac-Deltas, where the arguments are dependent:
$$A=\delta\left(a-\frac{b}{c}\right) \delta(a-b)$$ and $$B=\partial_a \delta\left(a-\frac{b}{c}\right) \delta(a-b)$$
As $A$ and $B$ are only nonzero when the arguments of the Deltas are zero, I tried to solve it this way: $a=b$ (from second Delta), thus $a=\frac{a}{c}$. Therefore I get $c=1$ as a restriction. I would rewrite $A$ then: $$A=\delta(c-1)$$
Is that correct? And can I handle the second quantity $B$ similarly?
Thanks!!