I need to verify that this is correct, if not could someone give me a hint as to what I need to do?
Thanks
Hello, robasc!
You used the Product Rule correctly,I need to verify that this is correct.
. . but you forgot part of the Chain Rule . . .
$\displaystyle g(\theta) \;=\;\sec\tfrac{\theta}{2}\tan\tfrac{\theta}{2}$
$\displaystyle g'(x) \;=\;\sec\tfrac{\theta}{2}\cdot\left(\sec^2\!\tfra c{\theta}{2}\cdot{\color{blue}\tfrac{1}{2}}\right) + \left(\sec\tfrac{\theta}{2}\tan\tfrac{\theta}{2}\c dot{\color{blue}\tfrac{1}{2}}\right)\cdot\tan\tfra c{\theta}{2}\quad\hdots\;\text{ etc.}$