AsTheDerivativeOfAFunctionOverAPowerOfASum​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

The derivative of U/V^k for V a sum with a logarithm of x in it, standing to the
power k + 1 below the bar of a single quotient: Rubi's
(a d n x^m - a d m x^m ln(c x^n) - b d n (q - 1) ln(c x^n)^q)/(x (a x^m + b ln(c x^n)^q)^2) is (d ln(c x^n)/(a x^m + b ln(c x^n)^q))'. U is a constant times one of the
monomials above the bar, tried in turn: the numerator W over the power must be
lambda (U' V - k U V'), decided at sampled points and then read monomial by monomial
with each power of x and of each function merged, so that ln(c x^n) ln(c x^n)^(q - 1) is ln(c x^n)^q as the integrand writes it; or null.