# Homework Help: Sticky differentiation

1. Feb 23, 2009

### captainjack2000

1. The problem statement, all variables and given/known data
I am trying to differentiate log((x+(x^2+y^2)^0.5)/(-x+(x^2+y^2)^0.5)) with respect to y

2. Relevant equations

I know that d/dx of ln(x) = 1/x but i am getting really confused when it comes to differentiating wrt to y?

Can I have some help please!

3. The attempt at a solution

2. Feb 23, 2009

### rock.freak667

Use the chain rule

$$\frac{d}{dy}= \frac{dx}{dy}*\frac{d}{dx}$$

So if you had to differentiate ln(x) w.r.t y

$$\frac{d}{dy}(lnx)= \frac{dx}{dy}*\frac{d}{dx}(lnx) = \frac{1}{x}*\frac{dx}{dy}$$

3. Feb 23, 2009

### djeitnstine

The argument is $$\frac{x+\sqrt{x^2+y^2}}{-x+\sqrt{x^2+y^2}}$$

So when differentiating with respect to y it looks like $$\frac{a+\sqrt{a+y^2}}{-a+\sqrt{a+y^2}}$$

where x is just treated as some constant a

So you just use the chain rule for that derivative

Does that look a little less confusing?