# Derivate of geometrical product

1. Apr 15, 2005

### Raparicio

Dear Friends

I'd like to know if anybody has the solution of the aplication of nabla's operator to geometrical product:

ab=a·b+a^b

And if it's possible to apply a operator like this:

d/dt + d/dx i + d/dy j + d/dz k.

My best reggards.

2. Apr 15, 2005

### quasar987

What is the geometrical product? Mathworld doesn't know.

About "d/dt + d/dx i + d/dy j + d/dz k". You wish to apply this operator to a scalar function? I don't know but the result would be a scalar + a vector. The operation of addition is not defined between those two identities afaik.

3. Apr 15, 2005

### Hurkyl

Staff Emeritus
It sounds a lot like the OP is working with quaternions... as a real vector space, their standard basis vectors are often written 1, i, j, k. The 1 is often suppressed.

It's also true that $a b = a\cdot b \vec{1} + a \times b$, where the first product is ordinary quaternion multiplication.

4. Apr 16, 2005

### robphy

Last edited by a moderator: Apr 21, 2017
5. Apr 17, 2005

### Raparicio

Thanks!!! very useful!