Differential Operators

Question

I'm unsure how to handle a calculation of the form (a*d/dt)(g(t)*d/dt). The paper I'm trying to improve upon had a and g as constants, so they circumvented dealing with the d/dt operators by just taking the LaPlace Transform and simplifying that way. I can reproduce that, but I now have a situation where the parameter represented by g *is* time-dependent and I'm struggling to figure out how to deal with operator notation. I would be eternally grateful to anyone who could help

Answer 1

Odd notation.

I'm guessing that it forms a differential equation. For example

ad/dt(g(t)d/dt)f(t) = adg/dtdf/dt + ag(t)d²f/dt²

If you are saying this is taken out of context of a larger derivative. would be interesting to see the full context.