Understanding Calculus: Is it OK to Just Memorize Theorems?

[Gablar16]

Well here I am studying calculus, and I've got to say that it is indeed pretty hard. All my experience with math up to pre-calc although hard work,it was relativly easy to "see". I can understand basic algebra good enough to be an algebra tutor at my school. I usually have no problems clearly visualizing algebra. Calculus has been a little different, I can't visualize the proofs in my textbook as easy as I did pre-calc or algebra. For example I'm learning diferential products but I don't really understand why the differential of a product = f(x)g'(x)+g(x)f'(x)

My question is, is it OK to learn calculus just learning how to use the theorems and maybe with use and practice I will "see" the why? I'm I just simply not smart enough?

I hope this is the right forum since it is academic advice. Thanks for any answers.

 

[leright]

Well here I am studying calculus, and I've got to say that it is indeed pretty hard. All my experience with math up to pre-calc although hard work,it was relativly easy to "see". I can understand basic algebra good enough to be an algebra tutor at my school. I usually have no problems clearly visualizing algebra. Calculus has been a little different, I can't visualize the proofs in my textbook as easy as I did pre-calc or algebra. For example I'm learning diferential products but I don't really understand why the differential of a product = f(x)g'(x)+g(x)f'(x)

My question is, is it OK to learn calculus just learning how to use the theorems and maybe with use and practice I will "see" the why? I'm I just simply not smart enough?

I hope this is the right forum since it is academic advice. Thanks for any answers.

Are you not understanding where the definition of the derivative comes from? All of the rules of differentiation are derived by simply substituting different functions into the definition of the derivative and then determining the result.

 

[Gablar16]

Thanks for your answer leright. I can understand that, but I can't see it clearly. I understand that the definition of the derivative has its roots on the definition of slope. I can see that fairly clear. the problem is that the theorems are comin in a little fast for me to clearly see how they all fit in the definition. Although applying the theorems seems "easy enough" so far it worries me that instead of understanding where the derivation of products comes from, I have to just assume the theorem is right and dumbly apply it. I guess with time and experience it will be fixed I just worry that when it comes time to apply the knowledge it will be more difficult than it needs.

Maybe it is just me worrying too much.

 

[Data]

Well, it's always a good idea to try to prove theorems yourself! If you can't figure out the proofs, then you can ask here or look online for help with them. Many people will be happy to help.