[sickufully]

I may or may not have one more question. But it's on derivatives. I'll assume you guys also know this stuff since you seem to know everything else.

We have to find dy/dx for each of the following.



Rules
if y = sinkx, then dy/dx = kcoskx
if y = coskx, then dy/dx = -ksinkx

The first one (vi) - I think it goes something like this:

y = 6sin(x/3) + 3cos(2x/3)
dy/dx = 6*(1/3)cos(x/3) + 3*(-2x/3)sin(2x/3)
dy/dx = 3/1cos(x/3) - 6x/3sin(2x/3)

Can I then simplify further to get:
dy/dx = 3cos(x/3) - 3x/1sin(2x/3)
or do I need to keep k as a fraction?



Rules
if y = e^kx, then dy/dx = ke^kx
if y = x^n, then dy/dx = nx^n-1

The second one (vii) - I didn't get very far. I think the first step is as follows, but I'm unsure of what to do next.

y = 3/x + e^3x/3 - 1/x^2
dy/dx = 3/1 + 3e^3x/3 - 1/2x
dy/dx = ???