Concise derivation? No, but the derivation(s) are sketched in my freely downloadable text Theoretical Evolutionary Genetics (just use the name as a search term). It is in Chapter VII.
A simpler way to explore this is to use Motoo Kimura’s 1962 formula for fixation probability with selection and genetic drift. When there is 1 copy of the allele initially, out of 2N copies of the gene in all, and the selection coefficient favoring the allele is s, the fixation probability is (1 - exp(-2s)) / (1 - exp(-4Ns)), where s can be either positive or negative. As s approaches zero from either side, the fixation probabilities approach 1/(2N), the value for a neutral mutant. Compute some values. Plot the fixation probability against s, say on a logarithmic scale on the s axis. Report the values to us.