solve(diff(-1/x,x) = (-1/x)^(b), b);
originally is 2, but it use ln(....) to express
if start from substitute, it seems need to replace manually.
solve(subs(a(x)=-1/x,diff(a(x),x) = (a(x))^(b)), b);
goal is to find b in equation below
solve(diff((x^2+x+1)/(-1+x)^2,x) = ((x^2+x+1)/(-1+x)^2)^(b), b);
solve(diff((x^2+x+1)/(-1+x)^2,x) = ((x^2+x+1)/(-1+x)^2)^(b), b);
(2*x+1)/(-1+x)^2-(2*(x^2+x+1))/(-1+x)^3 = ((x^2+x+1)/(-1+x)^2)^(b)
solve(diff((x^2+x+1)/(-1+x)^2,x) = ((x^2+x+1)/(-1+x)^2)*(b), b);