e^(t)cos(t), find first 4 terms centered at 0.

Alright, I know of two methods for doing this, and both seem remarkably painful.

I thought of listing 4 terms of each series (e^t and cost) and just multiplying them as polynomials and combining like terms. This wildly confuses me..

Then, someone recommended that I use derivatives to find the coefficients. Differentiating that function 4 times would be outright terrible.

Which way is the recommended?