Question

What is the unit of rate constant in a+b▶product dx/dt=k[A][B]

Answer 1

dx/dt is a derivative, hence a rate ;-)

[A] is the quantity of A
[B] is the quantity of B

The powers/exponentials on A & B are both 1, a 1:1 ratio... so that means what's left is... ;-)

Answer 2

dx/dt means the derivative of the independent variable x with respect to time

Something per time is called a rate. For example 300 m/s is the rate of 300 meters being traveled per every one second of time.

Answer 3

FYI if you need units for k, you'll need to first know the order of the reaction. (i.e.: depends on what reaction you're talking about)
http://en.wikipedia.org/wiki/Order_of_reaction

And then reference the units subsection of this:
http://en.wikipedia.org/wiki/Reaction_rate_constant

Hope this helps! ;D