Learning from a textbook without use of a truth table generator and natural deduction proof checker can lead to errors.
I will do the first one as an example.
If the answer isn't obvious, I would place it in a truth table generator to see if it is an equivalence. In this case it wasn't obvious to me so I entered the following into a truth table generator and found that indeed it was a logical equivalence.
At this point I could stop because I have shown the logical equivalence, but your question asks for a derivation and not a truth table. Here is one proof:
See the proof checker and the forallx text for details of how the proof checker works and the rules it permits one to use.
This provides a second way to get that first result, but you may be asked to use different rules and format them differently. However, you should be able to use the resources below to make those changes.
The other three problems can be approached similarly and I will leave them for you to explore.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
Michael Rieppel. Truth Table Generator. https://mrieppel.net/prog/truthtable.html