In

https://archive.org/details/in.ernet.dli.2015.59439/page/n109/mode/2up ,If k is the number of days in an industry's production period, x/w is the quantity of labor employed and (1/(1+i))^K*dF(x/w)/d(x/w) is the actual demand price of (x/w) labor, with (1/(1+i))=f(x), and (f(x)^k*(1/w)*(dF(x/w)/d(x/w)) , prove that kxf'(x)/f(x)*(dx/dw)=x(-1/w+((d^2F(x/w)/d(x/w)^2)/((dF(x/w)/(x/w))*d(x/w)/dw). any insight or help would be greatly appreciated.William