from these examples, it looks like you're struggling with the Chain Rule.
Any time you see a composite of functions, you will need to use the chain rule.
The way i remember it is "take the derivative of the outside (leave the inside alone), then multiply it by the derivative of the inside"

Let's do the 3rd one on the list step-by-step: y = cos (3x)

first, derivative of the outside, leave inside the parenthesis alone: d/dx(cos (3x)) = -sin (3x)
then, take the derivative of the inside: d/dx(3x) = 3

multiply them together: d/dx = -3sin (3x)

hope this helps

Okay I understand that pretty well. Can you show me how to do step-by-step one of the harder ones? Like the 4th one on the list?

#4 is a composition of 3 functions, so you will have to do the Chain Rule twice.
the three functions are the sec, the power, and inside the parenthesis

f(x) = 3 sec^2 (pi * x - 1)

I always start with the power:

d/dx 3 sec^2 (pi * x - 1) = 2(3 sec (pi * x - 1)) = 6 sec (pi*x - 1)

then derivative of the inside: (sec part)

d/dx (sec (pi*x - 1)) = sec(pi*x - 1)tan(pi*x - 1)

the the derivative of the 2nd inside part: (inside parenthesis)

d/dx (pi*x - 1) = pi

now multiply them all together:

(6pi)tan(pi*x - 1)sec^2(pi*x - 1)