Chain rule derivative with a log

[LukeT]

i have the equation - [math]ln(y) = ln(x(1+c)y(x))[/math]
Which i'm trying to work out the derivative with respect to ln(x), c is just a constant.

I can get as far as [math]dln(y)/dln(x) = (x(1+c)y(x) + x(1+c).d/dln(x)(y(x))/(X(1+c)y(x)[/math]
So i get that [math]dx/dln(x) = x[/math] and that because of the chain rule on ln the whole term ends up in the numerator, but i'm struggling to work out how to do the second part of the product rule specifically what [math]d/dlnx (y(x))[/math] is. Any help appreciated. Thanks

 

[Dr.Peterson]

i have the equation - [math]ln(y) = ln(x(1+c)y(x))[/math]
Which i'm trying to work out the derivative with respect to ln(x), c is just a constant.

I can get as far as [math]dln(y)/dln(x) = (x(1+c)y(x) + x(1+c).d/dln(x)(y(x))/(X(1+c)y(x)[/math]
So i get that [math]dx/dln(x) = x[/math] and that because of the chain rule on ln the whole term ends up in the numerator, but i'm struggling to work out how to do the second part of the product rule specifically what [math]d/dlnx (y(x))[/math] is. Any help appreciated. Thanks

Can you show us the original problem you are trying to solve, so we can be sure what this means, and whether what you're trying to do is the right thing? It's not clear, for example, whether "y(x)" means a multiplication, or just y as a function of x.

To untangle the complexity, I would probably define new variables, u = ln(x) and v = ln(y).