Is there a best way to study calculus problems

Reading your book from class is very important. Work the problems in the examples shown, and make sure you understand each step solved. After solving each example, go back and read the text again, and review the diagrams shown. Then solve the problem again to increase your understanding and skill in doing that type of problem.

Take good class notes, even if you don't fully understand what you are being shown at the time. You can go back over your notes later, and ask the teacher about anything you don't understand. If you still don't understand it, then ask your teacher if he or she will solve another problem like it, because you may see the point better with another problem of that type. Lastly, do your homework, and if you make any mistakes, learn from those. In my experience of going back to college several times again, I've noticed that most teachers compose their tests from class notes, example questions in the book, and homework.

When you first start out on calculus just remember a few important points:

d/dx f(x), written often simply as f '(x), is the slope of the tangent to curve f(x) at x.
if the tangent line is written as y = mx +c then f '(x) = m at the point where line meets f(x)

d/dx a.f(x) = a.f '(x)
d/dx (x^n) = n.x^(n-1)
d/dx (sin x) = cos x
d/dx (cos x) = -sin x

f '(x) = 0 where f(x) is a maxima or minima (called stationary points of f(x) )
practice curve sketching finding local SPs.

optimisation problems are usually geometric or financial, you need to do two things:
(a) either work out the function to optimise say area A(x)
(b) find solutions to A '(x) =0 and show that at each soln point x is max/min
you normal do this with nature tables.

as you progress further remember the product rule and function-of a - function rules,

d/dx (f*g) = f * g ' + f ' *g dont bother remembering division rule!