In: Physics
Answer:
Every person can able to derive physical equations on their own but it is based on their understanding on the particular concept or physical phenomena and their ability to use mathematical methods for the derivation of the equations. So important factors are basics of mathematics and proper understanding of physical concepts. Along with these factors one should have passion to derive the equations with patience. By regular practice people can train themselves effectively and they can able to derive the physical equations on their own.
To the second question, the answer is no. There is no harm to do research online to get information of other's work. There are many legal and secure ways to get required information to gain knowlegde. Now-a-days, every researcher using internet to get undates in their areas of research. One should use books along with online information to get excellence in particular area. The online information should be aunthetic or published by the recognized institution or organisation.