The chain rule written out in a nice organized way to understand.

Its a good thing the chain rule exists. It would be tedious to have to multiple out the bottom ten times even with pascal's triangle.

I think the chain rule can be easily over looked especially in a problem similar to this such as e^(3x)

This is because the trig function of tan has vertical asymptotes, so it would make sense for the inverse to have horizontal asymptotes at the same values.

It's kind of amusing how the derivative of anything that begins with the letter C has a negative value, so far

You can manipulate this a few ways to get a trig identity you need for a problem. An example would be if I need my terms to be in terms of cos and I had sin^2(y) in my problem, I would just replace sin^2(y) with -cos^(y)-1

I don't think we are ever supposed to cancel out a variable when we are solving for variables. Cancelling constants is fine because it just reducing or simplifying.

This reminds me of the u substitution method when solving derivatives

This is interesting. There wasn't a problem like this on the homework, but using the quadratic formula makes sense since nothing can be factored from each term.

This also happens at cos(θ) = 1, sin(θ) = -1 and sin(θ) = 1. These will only have 1 solution and whatever number of rotations are within the interval.

We can check this by trying to take sin inverse of 2 in the calculator. The result is an error.

An angle that can be found on the unit circle(π/6, π/4, π/3, and so on). Someone in class on Monday asked me what standard angles are.

This was an easy problem. It is called the unit circle for a reason. 1 unit radius

This problem is a lot longer than it looked at first. But it is important to go through the problem thoroughly to make sure we don't miss any solutions.

π/6 + 2πn, just means π/6 and each rotation of the unit circle. positive n going forward and negative n going backwards