Partial Derivatives of natural log

[nicolette2413]

Hey all. I'm having some problems with the partial derivatives of e. I understand the basics such as e^xy2. where I'm getting confused is with the following

dz/dx=e^(x+y)

and

dz/dx=1/e^x+e^y

Can anyone help me out with understanding these??

 

[HallsofIvy]

Hey all. I'm having some problems with the partial derivatives of e. I understand the basics such as e^xy2. where I'm getting confused is with the following

dz/dx=e^(x+y)

and

dz/dx=1/e^x+e^y

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 e^x+y and 1/(e^x+ e^y or are you saying these are the derivatives and you want to find z?

Can anyone help me out with understanding these??

 

[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 don't contain "e" but these I am having problems grasping.

 

[HallsofIvy]

Do you know what the derivative of e^x is? The ordinary derivative, not partial derivative. It's the world's easiest derivative!

Do you know what the derivative of Ce^x is? e^x+y is e^xe^y.

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

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

 

[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=(e^x+y)/(e^x+e^y)

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=(e^x+e^y)(e^xe^y)-(e^xe^y)(e^x+e^y)/(e^x+e^y)²
dz/dy= the same as above.

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

 

[HallsofIvy]

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=(e^x+y)/(e^x+e^y)

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

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=(e^x+e^y)(e^xe^y)-(e^xe^y)(e^x+e^y)/(e^x+e^y)²
dz/dy= the same as above.

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

The derivative of e^xe^y with respect to x is just e^xe<sup>y 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.)</sup>

 

[nicolette2413]

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