Help with Beginner Index Notation

[fttteotd]

Okay, so I'm learning some basic index notation, and I have a few questions...

Homework Statement

f= scalar field
F = vector field

so, we are supposed to show that curl(fF) = fcurl(F) + ($$\nabla$$f) x F

The Attempt at a Solution

curl(fF) = [$$\nabla$$ x (fF))]$$_{k}$$ = $$\in$$$$_{ijk}$$(f$$\partial$$$$_{i}$$F$$_{j}$$ + F$$_{j}$$$$\partial$$$$_{i}$$f)

any help??

(all the superscripts are supposed to be subscripts, i dunno)

 

[tiny-tim]

Welcome to PF!

Hi fttteotd! Welcome to PF!

(have a curly d: ∂ and a nabla: ∇ and an epsilon: ε and use itex rather than tex in the middle of a line )

[∇ x (fF)]_i = ε_ijk∂_j(fF_k) …

and now use the chain rule!