Here I am going to take a look at some of the most common mistakes made by calculus students and how to avoid them. There are some mistakes that are specific to calculus that are very common, like not fully understanding the chain rule for derivatives (which leads to many mistakes in many areas of calculus), forgetting the constant when finding indefinite integrals, and coming into a calculus sequence with very rigid assumptions about how math works. Additionally, there is a specific mistake that can be made in any academic area that is particularly bad in calculus. That mistake is getting behind in the material because of procrastination. Let's take a look at each of these mistakes individually, see why they are so important to avoid, and what you can do to keep from making them.

Early in the calculus sequence, the single topic that gives the most students the most trouble is using the chain rule for derivatives. The chain rule is a way to handle the derivatives of composite functions, and is one of the things from the beginning of calculus that will be used consistently throughout the calculus sequence. If you don't understand the chain rule extremely well, then you will often find yourself being completely lost when taking complicated derivatives later in the course. To avoid falling into this trap, make sure to spend extra time working on the chain rule. You could even ask your instructor or fellow students to come up with difficult composite functions for you to take the derivative of to practice.

People who begin a calculus course tend to be good math students who have rarely had to put in a lot of effort to do well in math classes. Calculus is a different beast than algebra or statistics because you cannot just rely on your general problem-solving abilities to get you through. The topics in calculus are much more abstract than the concrete ideas of previous math classes you would have taken, and good students often find themselves in a position where it takes a week or two before they fully understand a certain idea or concept in calculus. Because of this, you have to keep up with the course work and study as you go. If you're already two weeks behind, and then get stuck on a certain idea and end up another two weeks behind, then you'll be too far behind in the course to ever catch up.

Another topic that's specific to calculus is finding indefinite integrals. Later on in your math career, you will discover that being able to take an integral is one of the most important skills in all of advanced mathematics. Students often forget the constant at the end of an indefinite integral because it doesn't stick out in their mind as being particularly important. Unfortunately for them, it is terribly important, and forgetting it is a much bigger mistake than they realize. For this reason, you should place special emphasis on the constant term of indefinite integrals and try to never forget it.

When you come into a calculus course, you will have already had years of math experience, mostly in algebra, under your belt. Because of this experience, you will have some basic assumptions about how math and the physical world operate. Some of the things you learn in calculus will change a lot of these assumptions, especially when it comes to things like how infinity and negative infinity work. If you aren't open-minded and capable of re-evaluating what you think you know, then you will have a lot of trouble learning calculus and performing well on assignments.

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