f(exp(1/12 (-12 log(A) + 5 log(x) + 1 - 6 log(2 π)) - 1/(156 x^13) + 1/(144 x^12) + 691/(360360 x^11) - 691/(327600 x^10) - 1/(1188 x^9) + 1/(1056 x^8) + 1/(1680 x^7) - 1/(1440 x^6) - 1/(1260 x^5) + 1/(1008 x^4) + 1/(360 x^3) - 1/(240 x^2) + 1/4 x^2 (2 log(x) - 3) - 1/(12 x) + 1/2 x (-2 log(x) + 2 + log(2 π))))

d/dx(f(G(x))) = 1/2 G(x) (-2 x + 2 (x - 1) polygamma(0, x) + 1 + log(2 π)) f'(G(x))