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Is there a specific reason why they wrote (F' * f)' instead of (f * f)' ?

I've posted a solution at the bottom of the post but I don't understand the first step: (F' * f)' = F'' * f.

Is this some standard trick that always applies?

The way I would write is \(\displaystyle f' * f = ( 2\theta(t) + \delta(t) ) * (2t+1)\theta(t)\), I dont see how it becomes what is written in the solution.

If someone knows of any good sources where I can read up on convolution it would be awesome if you could direct me there. Right now I only vaguely understand what convolution is (I would say: sliding two functions across each other and creating a third one by summing the overlapping area for each time unit).

I'm trying to get started on the mathematical calculations but I find it hard to grasp.

Solution: