# Differentiation of dot product using cartesian components

1. Nov 12, 2008

### CmbkG

1. The problem statement, all variables and given/known data

Show using cartesian components that

d/dt(a.b)=(da/dt).b+a.(da/dt)

3. The attempt at a solution

a= axi+ayj+azk
b=bxi+byj+bzk

a.b=axbx+ayby+azbz

d/dt(a.b)= d/dt(axbx+ayby+azbz)

2. Nov 12, 2008

### HallsofIvy

Staff Emeritus
Okay, so go ahead and do that! Use the sum rule and product rule.

3. Nov 12, 2008

### CmbkG

So ive done that nd nw iv got

(da/dt)b+(db/dt)a

do i just put this as the dot product or have i missed out something in my equation?

4. Nov 12, 2008

### Pere Callahan

Since you're talking about putting this as a dot product I assume by writing (da/dt)b you meant some different "product" of the two vectors da/dt and b. May I inquire what exactly you were thinking of and how it is related to the dot product (which is where you started from.)

5. Nov 12, 2008

### CmbkG

oh, i see now, i wasn't thinking of them as two vectors but as mulitplying two scalars.

i just forgot what it was i was working with, sorry.

Thanks alot for your help though, really appreciate it.

6. Nov 12, 2008

### Pere Callahan

It sometimes happens to be useful to pay attention to exactly this particular issue