First, just set up the problem and what we are looking for. We have and we are trying to find;
Starting with , we start with
and what is partial-P over partial-L? - Well, capital-P isn't a direct function of capital-L, we'll therefore need the chain rule to get through the intermediate variables inside 
Going throw the terms inside the brackets one-by-one,
l we don't know -- if we were given a functional form for we could probably find it, but for now we'll just leave it as 
is pretty simple, given , it's just .
isn't known. Given a functional form of we could probably solve for it -- but now we'll just leave it at is.
We are told to assume that k is independent of L & h. Which implies that .
Great, so we can rewrite the above as; which further simplifies to the follow,
Now let's find 
Now let's break open 
Now we're going to go through each one of those four terms inside the bracket;
 isn't known to us now. If we were given a functional form for P, we could probably find it easily. But for now we leave as is.
 - since we are told that  , this implies that
 isn't known to us now. Again, if we were given a function form for P, finding this term wouldn't be too hard. But for now we leave it as is.
 , since we were told in the question that k is independent of h (and L).
This means that the above terms simplifies into the following;
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