I don't even know where to begin on this one. It's not (xtanx)2^(xtanx-1) is it?
You need to know, first, that the derivative of is . Further, by the chain rule, the derivative of is .
In this case, of course, u(x)= x tan(x). Use the product rule to find du/dx.
(Once again, Soroban beats me by 1 minute!!!)
Some of the posters in this thread seem to think that calculus is an exercise in the memorisation of a fist full of "rules".
Here you need the definition of logarithms and a bit of manipulation:
Then the rest follows from the systematic application of the product and chain rules and a table of basic derivatives.
Brain storage space is to precious to waste on large list of rules, understanding acts as a compression algorithm, the more you understand the less you need to remember.
Also rule based rote learning gives the wrong idea to the student of what mathematics is. I don't care if the student manages to clear artificial hurdles what I do care about is that they learn to appreciate what maths is about (beauty and pattern) and can use what they do know in novel situations.