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.
To answer your question without being a dickhead: The given x indicates the point on the curve you need to find the slope at. In other words, find the derivative and then evaluate that function at the given x.
It is a partial derivative. Apparently you haven't taken Calc III. I figured that would be basic math for most people. It is a shock to me that a person studying to be a nurse doesn't need a degree in math.
Never mind. I misunderstood your question. Also I was joking about the calc III is basic part