Am I right in assuming this is a cross product? if so, you need to use the formula:
and then differentiate the remaining function with respect to t. so for example, when multiplied the i vector becomes 2ti and hence, when differentiated becomes 2i. then repeat using the formula for j and k above and differentiate each term (remember that e1 is i, e2 is j ad e3 is k). this should give you the answer to the first part of the question.
For the second part, differentiate B : so B= 6t^2i - k
Then multiply this by A using the formula above. And then differentiate each term as in the first part.
Does this make sense? I have deliberately left the answer out so that you can have a go but if it gets difficult I can give you more detailed working