This is pretty much just a yes or no question (an explanation on top would probably help though).
I'm asked to find the derivative of the following generating function:
$$ G(x,r) = \sum_{n=0}^\infty P_n(x) r^n = (1 - 2rx + r^2)^{-\frac{1}{2}} \quad \quad |x| \leq 1, \ |r| < 1.$$
I asked a question on integrating this function previously: Re-arranging and integrating a Generating Function of Legendre Polynomials
My main confusion on this question was that I didn't know that we didn't have any dependency on $r$ so we could just ignore it.
My question is; does the same apply for finding the derivative? Do I ignore the $r$ terms when finding the derivative or keep them in?
I've calculated the derivative with the $r$ terms included as $r/{(1-r(2x-r))}^{3/2}$ but this doesn't look quite right so I'm leaning more towards just ignoring the $r$ terms, could anyone clarify what I should do?
Thanks in advance