It's been nearly 35 years since I did uni level calc and I've not really used in the the years since - fucked if I could figure it out without a lot of <insert search engine of choice> foo these days
That requires neither engineering-level math nor paper nor patience. All you need is the chain rule and some basic knowledge of sine and cosine:
The derivative of cos is -sin, but because of the 6x you get an extra factor 6. The sine function is periodic on 2pi, so sin(6*2pi + pi/2) = sin(pi/2) = 1. So the result is -36
My "advanced" maths course did (from what I could tell) the exact same as the basic one and we started calculus before the classes were split, the only issue would have been the notation and half the class not paying attention.