I am very interested to know how they derived the formula in the hint of the question [tan (s)= r dr/d(theta)]. I made an attempt, but I do not no how to proceed from here. And can you advise me some books so that I can get a better idea of how to derive formulas like these, using infinitesmals (dx, dy, dr) etc. Thank you for reading.

P.S. I can solve the problem using the formula. I can't derive the formula by myself.