Vector calculus product rule for derivatives of N

[Shackleford]

I'm honestly totally clueless on 4 and 10. For #4a, I plugged in dN/ds and used the product but didn't see a solution. I did something similar for 4b. I also don't see how the two hints help. For 10, I multiplied f and the two vectors, tried to find the divergence, used the product rule twice, I believe. Sorry I don't have my notes scanned for these two.

Here are some notes related to #4, I imagine.

 

[vela]

The hints for 4a and 4b suggest you differentiate those expressions (the ones in the hints) with respect to s.

For problem 10, you want to use the identities for $$\nabla\cdot(f\vec{A})$$ and $$\nabla\times(f\vec{A})$$. They should be in your textbook somewhere.