# Homework Help: Partial with respect to ln(f(x))

1. Oct 11, 2011

### TheBestMilk

1. The problem statement, all variables and given/known data
I'm working a problem, and I've come to taking the derivative with respect to ln(x):

$\frac{\partial ln(x^{c})}{\partial ln(p_{x})}$

2. Relevant equations

ln(x$^{c}$)=ln(p$^{2}_{y}$I)+ln(p$_{x}$+p$_{y}$)-ln(p$_{x}$)-ln(p$_{y}$)

3. The attempt at a solution
I've worked it out, but am not sure how the ln(p$_{x}$+p$_{y}$) term would derive with respect to ln(p$_{x}$). Any help would be great. Thanks!

$\frac{\partial ln(x^{c})}{\partial ln(p_{x})}$ = $\frac{\partial}{\partial ln(p_{x})}$(ln(p$_{x}$+p$_{y}$)) - 1

2. Oct 12, 2011

### CompuChip

Probably you can use the chain rule here, finding a convenient "intermediate" variable, e.g.

$$\frac{\partial \ln(p_x + p_y)}{\partial \ln(p_x)} = \frac{\partial \ln(p_x + p_y)}{\partial p_x} \cdot \frac{\partial p_x}{\partial \ln(p_x)}$$

looks like I could do it