Thanks everyone, you all helped :)
Tiggsy, I can follow what you have done and I can see that early on I/you had already determined that
d/dx secx = tanx secx
I suppose that the bit that is still troubling me is multiplying by (secx+tanx)/(secx+tanx)
I mean I can see that it works but I would not think of it ... is there something I am missing, I mean a hint of what to do or something? Is this just a 'trick' that I must commit to memory for questions such as this?
Is there some extra working that can be thrown in to make it more obvious?