Re: Directional Derivative

is the normal vector. It can be pointing in or out of the sphere, whereas points out of the sphere.

Re: Directional Derivative

As far as I know, |x| is NOT a vector.

Re: Directional Derivative

**n** = x/R**i** + y/R**j** + z/R**k**

**del**f = *d*f/*d*x**i** + *d*f/*d*y**j** + *d*f/*d*z**k** = *d*f/*d*x**i**

df/dn = **del**f.**n** = (*d*f/*d*x)x/R

IxI = R only at a point where sphere crosses x axis, in which case

df/dn = df/dx, for x pos

Re: Directional Derivative

I think there is a misunderstanding here. By a function of several variables I mean explicitly

,

so that

is the euclidean length of .

I thought this was clear. Anyway, it's my fault. Sorry.

Re: Directional Derivative

The notation is somewhat arbitrary as long it is clear from the context what it means.

Since you said it was a directional derivative in the direction normal to the sphere, I would interpret your derivatives to mean:

Although it may also be possible that your vectors need to be normalized, depending on how your book defines a directional derivative.

See Directional derivative - Wikipedia, the free encyclopedia for more information on how a directional derivative is or can be defined.

Either way, those 2 forms are the same, except for a possible minus sign.

Re: Directional Derivative

OK, that was easier than I had thought!

My problem was the normal derivative of a function on with radial symmetry, i.e.

.

Now it's clear that for we have

Oh my! Simple as that! (Headbang)

Re: Directional Derivative

That looks about right. :cool: