Right now I'm seeing multivariable calculus and differential equations. I can apply all the rules they teach in class and solve all the problems with the correct "method". However, I'm starting to worry that I don't know how to prove anything! For example, if I were teaching implicit differentiation in multivariable calculus to someone else, and that person asks me "why is it this way?" I would either tell them "you see, in leibniz notation differentials seem to cancel out" or just simply say "I don't know". Why is the derivative of sinx=cosx ? I dont know! Is my limited ability to prove things in calculus indicative of how little I know? Is it important to be able to prove things in calculus? Or are these things "stupid details" that if I took the time to do the limits I would see where they come from? Can anyone tell me what's the normal relationship one has with calculus? I study physics btw. Thanks.