I'm teaching myself because I'm transferring to a new college as a junior, and I want to major in physics/chem (previously undecided). i thought it if learned enough i could test out of the first couple courses (like one and two, or just one at least). basically, i have a book that gives the concepts then gives you a bunch of exercises. with the derivatives, i have basic shortcuts given (d/dx sin x= cos x, d/dx cos x=-sin x, etc.) then i do a bunch of problems, like 15. same for the inverse functions. the issue is, i don't feel like i fully get it. like intuitively, i can see how d/dx sin x= cos x just by following the slope of the sine graph, but algebraically i can't derive it from the difference quotient, and i don't really know any of the trig identities.