From the factory, the following fluids are synthetic, and the service manual specifcally states to use synthetics:
Transmission (ATF+4), transfer case (ATF+4), power steering (ATF+4), rear axle (75W-140), Getrag 238 manual transmission (ATF+4).

This leaves the front axle and engine oil. (And the blinker fluid )

You can change to any synthetic oil you want. Some people like Royal Purple, some like Amsoil, some like Mobil 1.
And fan-boys of any of them can spurt articles out their rear-ends about "how great _____'s product is, and _____'s product just doesn't match up." Blah, blah blah.

 

hmmm

Thats weird, because I just checked and Dodgerules86 is right, for AMERICAN driven dakotas. My damn Canadian manual says I have to use synthetic for both the front and back. Maybe has something to do with winters or something.... which I still could not understand. None the less, I got it done, it was only $200.00 with a good ole oil change. The manual serivce, I usually go for the longer one, as I am all hiway driving with no conditions they state for the 5000 kms oil change etc. But.... To play safe after reading the post on here about the rear end going on a guys truck, I was not willing to risk giving a reason to dodge to not warrenty the work should something ever happen. I am sure, that is not cheap to get fixed.

 

The term 'synthetic' first need to be defined.

API group IVoils are 'true' synthetics as they contain no mineral oils.
Group III oils are mineral oils that have been hydrocracked/hydroisomerized and arelabeled and sold as synthetic in the US even though they are not 'true' synthetic.

Now you can find out if your 'synthetic' oil is really synthetic or not...