I've been bumping up against the transcendental function H^(-1)(x), the inverse of the binary Shannon entropy function:
H = -(xlogx + (1-x)log(1-x))
and now a friend of mine is trying to calculate a closed-form solution to a derivative involving the inverse function (attached).
Can Mathematica do approximations to solutions involving transcendental functions, like "solution-fitting?" I've attached his scenario as a pdf.
Attachment: derivative_binary.pdf, URL: ,