The first looks to be a simple application of the product rule...
This is really starting to irritate me as I can't seem to get anywhere with it:
I need to solve somthing similar to a trigonometric identity but using the definition of grad,div and curl to verify:
I have no idea where to begin, I have the definitions but I fail to see how they can help me, can anybody can help me?
If you know the definitions, why not use them to do what is shown on both sides? For example, you should know, from the definition, that . Now use the product rule as Prove It suggested.
And be careful how you write the second one. You have one "f" where you mean "F" but more importantly you have written " " and " " where I think you really mean and .
Do you mean that
, where and are scalar functions?
if so, we note that for the i component of the LHS is . Where denotes the i component of
Now using the formulas for curl and gradient, we may calculate the RHS and simplify it in order to get it to look like the LHS.
Note the ith component of is