# Homework Help: Partial derivative chain rule for gradient

1. Jan 6, 2013

### physics2000

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

$$ln(z / (sqrt(x^2-y^2))$$

2. Relevant equations

$$∇=(∂/(∂x)) + ... for y and z$$

I just want to know how to do the first term with respect to x

3. The attempt at a solution

I am so rusty I dont know where to begin.

2. Jan 6, 2013

### e^(i Pi)+1=0

$ln(z) - \frac{1}{2}ln(x^2-y^2)$

That ought to make it easier. Now treat y and z as constants.

3. Jan 7, 2013

### cosmic dust

You don’t sum... Gradient is a vector and what you have found are the linearly independent components of it.

4. Jan 7, 2013

### Fredrik

Staff Emeritus
jfgobin, you shouldn't give away the final answer when you're answering posts in the homework forum. Just give a hint, like e^(i Pi)+1=0 did.
Mod note: I dealt with this.
physics2000, The hint given by e^(i Pi)+1=0 simplifies the problem significantly, but you don't have to use it. It's also possible to use these three rules directly:
\begin{align}
&\log'(x)=\frac 1 x\\
&(fg)'(x)=\frac{f'g-fg'}{g^2}\\
&\frac{d}{dx}x^a=ax^{a-1}
\end{align}

Last edited by a moderator: Jan 7, 2013
5. Jan 7, 2013