Hey all, I'm working on this problem for my economics. Although it's economics and not "math", the steps involved shouldn't require any knowledge of economics. It involves logarithms and elasticities and derivatives, but I'm having a bit of trouble getting the solution. We've been given the answer (Theta/1-Theta). The question is asking to "derive the elasticity of steady-state output per worker (y) with respect to the saving rate (s)". Now for the record, if it helps, that in the steady state, the growth rate of y is 0 (it is constant). This is the equation as presented.
Now the first step I was told by my professor was to take the logs. So I did that, and I come up with. For the record, I replaced theta with "a" and the depreciation with "x", as I didn't have access to those at the moment.
From here though, differentiating with respect to ln(s), I cannot for the life of me figure out where to get the (a/(1-a)) from.
Also of note, the formula for elasticity for example with X and Y, is (X/Y) * (dY/dX) if it helps to work with the first equation.
Any help is appreciated.