Well it's not clear what the expression is. Use LaTeX. If the expression is what I think it is, then you haven't done anything at all to it.
It would help if you used more parentheses. The "composite" rule, I would think of as involving composite functions: f(g(x)) but what you have written appears to be (e^x) ((2/3)sin(x)) rather than the composite e^((2/3)x sin(x)). In any case, you don't seem to differentiated at all! You final "answer", 2(e^x)(sin(x))/3, is just the original function. What is the derivative of that function?
This now says is that what you intended?
I have no idea what you mean by this! it is certainly NOT the function above. Did you mean that as f'(x)? It is not for either or .f(x)=e^x(2/3sin(x) (2/3sin(x))
If you meant , its derivative is itself, times the derivative of which is NOT .=e^x(2/3sin(x) 2/3cos(x)
=2/3cos(x) e^x(2/3sin(x))
I'm stuck on trying to differentiate f(x)=e^x(2/3sin x) as well and I've tangled myself up into a complete mind block! I think it's the 2/3 aspect confusing me the most, I've never been quite sure what to do with fractions when they pop up like this in functions. D'oh. Any help/advice would be much appreciated!