Re: Directional derivative

Quote:

Originally Posted by

**Ulysses** Hi there. I have to find the directional derivative for:

at the point

in the direction of

.

The thing is that the derivatives for this function are not defined at the point P0. So, I can't use the proyection of the gradient over u. But using the definition I've found an answer, I think its right, but I'm not pretty sure, because the function is not well defined at the point it's asked.

This is what I did:

So, the thing is if this is the right answer, or if I should say that the derivative at that point doesn't exist.

Well, assuming that you did this right then the directional derivative doesn't exist because that limit you wrote doesnt.

Re: Directional derivative

The limit does not exist,

Edited: Sorry, I didn't see **Drexel28**'s post.

Re: Directional derivative

Quote:

Originally Posted by

**Ulysses** Hi there. I have to find the directional derivative for:

at the point

in the direction of

.

The thing is that the derivatives for this function are not defined at the point P0. So, I can't use the proyection of the gradient over u. But using the definition I've found an answer, I think its right, but I'm not pretty sure, because the function is not well defined at the point it's asked.

This is what I did:

So, the thing is if this is the right answer, or if I should say that the derivative at that point doesn't exist.

Suppose you calculated the required directional derivative at the point where then took the limit as and .

CB

Re: Directional derivative

Thank you all, I forgot the absolute value :P

Re: Directional derivative

I've been thinking about this, shouldn't I take the limit only in the positive direction considering than that direction is the one pointed by the vector given? I mean taking this limit only:

Re: Directional derivative

No, it is . :)