# Partial Derivatives of natural log

1. Nov 12, 2008

### nicolette2413

Hey all. I'm having some problems with the partial derivatives of e. I understand the basics such as exy2. where I'm getting confused is with the following

dz/dx=e(x+y)

and

dz/dx=1/ex+ey

Can any one help me out with understanding these??
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 12, 2008

### HallsofIvy

Staff Emeritus
I don't understand what you are asking. You ask about finding the derivative but then give the derivative. Are asking for the partial derivatives of ex+y and 1/(ex+ ey or are you saying these are the derivatives and you want to find z?

3. Nov 14, 2008

### nicolette2413

I'm sorry for being confusing. Yes I'm thrying to find the partial derivative of each item. I have no problems with partial derivatives that dont contain "e" but these I am having problems grasping.

4. Nov 14, 2008

### HallsofIvy

Staff Emeritus
Do you know what the derivative of ex is? The ordinary derivative, not partial derivative. It's the world's easiest derivative!

Do you know what the derivative of Cex is? ex+y is exey.

1/ex+ ex= e-x+ ex.

Those are both easier than $e^{xy^2}$!

5. Nov 16, 2008

### nicolette2413

I guess I'm not asking this very well. I'm trying to solve the problem in parts but that's not helping me understand this any better. The full problem is...

z=(ex+y)/(ex+ey)

And I need to find the partial derivatives in respect to "x" and "y"
I am coming up with an answer that fully cancels out and winds up being zero when added back together.

Here's my work...

dz/dx=(ex+ey)(exey)-(exey)(ex+ey)/(ex+ey)2
dz/dy= the same as above.

I'm sure I'm missing something, but can't find where. Can you help please?

6. Nov 17, 2008

### HallsofIvy

Staff Emeritus
It is always a good idea to state the entire problem!

The derivative of exey with respect to x is just exey again and I think you have that in your answer. But the derivative of ex+ ey is just ex because ey is a constant with respect to x and its derivative is 0.

dz/dx=(ex+ey)(exey)
is correct
-(exey)(ex+ey)
this is wrong. You should have -(exey)(ex)
(the denominator was correct so I didn't mention it.)

7. Nov 17, 2008

### nicolette2413

Thank you, now that you pointed out where i was wrong, it makes much more sense!