I am checking out an interesting paper regarding applying a chain rule for distributional derivatives. The paper is here.
I would like to solve the given problem by this chain rule, but I am not sure how to proceed:
Find the solution to the given derivative of the product $$\big(\cos{x}\delta(x)\big)^{(k)}$$
If I set $u=\big(\cos{x}\delta(x)\big)$, and $\frac{du}{dx}=\cos{x}^{(m)}\cdot \delta(x) + \delta(x)^{(m)}\cos{x}$, that doesn't work out, since $m=0,1,2,....$.
Any suggestions welcome!
Thanks