Partial derivative of function w.r.t. the percent change of the variable

Usuiisu

Hi,

It is common to consider taking a derivative of % change in function w.r.t the % change in the variable:
∂(%Δf(x,y))/∂(%Δx) = ∂logf(x,y)/∂log(x)= ∂f(x,y)/∂x*x/f(x,y).

But how do you take the partial derivative of the (level of) function w.r.t the
% change in the variable?
I got to this much:
∂f(x,y)/∂(%Δx) = ∂f(x,y)/∂(d log(x) ).

I found the % change in x can be written as the differential of log(x), but I don't
know what to do the next. I want to write it in terms of f, ∂f/∂x, x.

Thank you very much in advance.