I don't even know where to start on this problem, how do I solve this?
Starting out the problem is always the most difficult part, I find it extremely helpful to go through the problem and write out any useful information it gives you, write out any of these quantities and then write out all the useful relations in this particular area. Then you want to write what you ultimately want to solve for or find. At the very least it'll get your gears going and you may be able to see how to use the relations to get your desired answer.
How do I simplify logarithmic functions?
Well, it's best to firstly recall (and even list out) all of the important logarithmic properties we may need in simplifying. These properties are key to understanding how logarithms work and when you have them written out, it is a lot easier to see how to use them in any particular case. Once you have them down, apply them to the problem at hand, after doing this enough times, it'll become natural!
How can I understand, more clearly what I am doing when I am taking a derivative?
Everyone understands things in their own way, so we can look at it from different points of view and see what makes the most sense to you. We can look at it graphically, what exactly the derivative represents, we can look at it as its definition with limits, and we can look at examples so that you can both understand what it is you're calculating and why it's important, and so that you can get into the rhythm of calculating them.