Vector Analysis Help: #4 & #10

[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.