I was looking at the Bessel Function of the Second Kind, $Y_n(x)$
http://www.wolframalpha.com/input/?i=bessel+function+of+the+second+kind
http://mathworld.wolfram.com/ModifiedBesselFunctionoftheSecondKind.html
http://www.math.usm.edu/lambers/mat415/lecture16.pdf
and found that it's derivative is $$\frac{d}{dx}\left(Y_n\left(x\right)\right)=\frac{1}{2}\left(Y_{n-1}\left(x\right)-Y_{n+1}\left(x\right)\right)$$ I'm still not sure if the Derivative of the Bessel Function of the Second Kind can be expressed in terms of $x$, using elementary functions, when $n$ is either an integer or half integer.
Is it possible to express the Derivative of the Bessel of the Second Kind in terms of $x$ using elementary functions when n is an integer or half integer? If so what is the method to figure out the elementary functions that the Derivative of Bessel Function of the Second kind is expressed in for any integer or half integer value of $n$?