Partial with respect to ln(f(x))

[TheBestMilk]

Homework Statement

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})}

Homework Equations

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

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

 

[CompuChip]

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

<br /> \frac{\partial \ln(p_x + p_y)}{\partial \ln(p_x)} = <br /> \frac{\partial \ln(p_x + p_y)}{\partial p_x} \cdot<br /> \frac{\partial p_x}{\partial \ln(p_x)} <br />

looks like I could do it