TITLE: Why is calculus considered to be difficult?
QUESTION [6 upvotes]: I am going to take a calculus course soon and everyone tells me that it is very difficult. What is considered difficult about it and why do so many people fail in calculus courses?I am asking these questions so that I can prepare myself beforehand and do not face any difficulties which most people face.

REPLY [3 votes]: When you first learn arithmetic, adding / subtracting / multiplying / division / exponentiation / roots ... that seems hard at first.  With practice, it gets easier.  Multiplication is just repeated addition.  Exponentiation is just repeated multiplication.  As such, you could say that multiplication is just "meta" addition (it takes addition as a starting point and builds on it), exponentiation is just "meta" multiplication, roots are just "meta" division.
Many people can do these based on rote (memorizing multiplication tables, etc.).  They don't have to go looking for patterns.  So they never do.
When you're studying algebra, the arithmetic is used but it's "background" compared to what you're learning.  Instead of doing those things on numbers, you're doing the on numbers and variables.  And you're finding meta-patterns which can be useful "shortcuts" for arithmetic
Pop quiz: what's $41 \cdot 39$? Gee, that's $(40 - 1)(40 + 1)$ which is $40^2 - 1$
In that regard, algebra can be seen as "meta" arithmetic.
If your mind isn't already looking for "meta," algebra is difficult and everything above it is even more so.
Trig / pre-calc introduces you to functions, including the usual sine / cosine/ tangent and logarithm.  This function applied across this entire expression gives you this other expression ($sin(2\theta) = ?$).  This expression using this function can be expressed in this other way, which may be easier to solve.  Logarithms are just "meta" exponentiation / roots.
Calculus is meta algebra.  You're not just manipulating numbers (arithmetic), variables (algebra) and functions (trig / pre-calc).  You're manipulating entire formulas / expressions which use ALL of the above.  Doing a differential (derivative) or an integral on an equation gives you a different equation, with useful properties relative to what you started with.  The rules for getting from A to B ... that's really hard to do by rote.  You need to be looking for patterns, learning those, learning how to apply those.  You're not just going "meta," you're going "meta" on something which is already "meta."  And that can be a big leap.
If you have an easier time with the lower-level stuff, your mind likely has already started looking for the meta-patterns in those lower levels.  Calculus likely won't be such a stretch for you.
If your mind isn't already looking for meta-patterns, calculus can be really tedious.  In my experience, the vast majority of people are NOT looking for meta-patterns, which can account for why so many people struggle with calculus and, indeed, any of the higher math.
This is further compounded by the fact that calculus tends to be taught as a stand-alone topic.  If you aren't taking physics at the same time, you end up with one overriding question ... when am I EVER going to use / need this? And we tend to discount things we don't think we'll use / need.  That's just human nature.  Consequently, if you are taking calculus, try to see if you can get a physics class at the same time.  I was lucky in that I was able to take both, concurrently, in High School.