determine the derivative of $\displaystyle y=3e^{sin(x+2)}$
Yes that is the chain rule and it's the only way to solve this question.
Archie Meade's way is best
If you let $\displaystyle u = \sin(x+2)$ then you can find $\displaystyle \frac{du}{dx}$ without much difficulty (although you're using the chain rule the derivative of x is 1 so it makes no numerical difference in this case)
Thus you have $\displaystyle y = 3e^u$ which you should know how to solve.
I must stress that this is still the chain rule though