# Partial derivatives of a function

1. Oct 22, 2011

### Mr.Rockwater

1. The problem statement, all variables and given known data

Find the partial derivatives (1st order) of this function:

$ln((\sqrt{(x^2+y^2} - x)/(\sqrt{x^2+y^2} + x))$

2. Relevant equations

3. The attempt at a solution

I obviously separated the logarithm quotient into a subtraction, then applied the rule d ln(u) = 1/u. However, what I end up with is four terms with a bunch of x²+y² and $\sqrt{x²+y²}$ . I'm just starting out with partial derivatives so is there any obvious trick that I'm not familiar with in this type of situation?

Last edited: Oct 22, 2011
2. Oct 22, 2011

### sandy.bridge

You were on the right track.
$ln((\sqrt{(x^2+y^2} - x))-ln((\sqrt{x^2+y^2} + x))$
You can now take the partial derivative of this function with respect to x, then respect to y.

remember:
$$\frac{\partial ln[f(x, y)]}{\partial x}=\frac{1}{f(x, y)}\frac{\partial f(x, y)}{\partial x}$$