What concepts were most difficult for you to understand in Calculus? [closed]

I'm developing some instructional material for a Calculus 1 class and I wanted to know from experience for yourself, tutoring others, and/or helping people on this site where is the most difficulty in Calculus?

If you had any good methods of helping people that would be very helpful.

The hardest thing for me was to understand what is meant when someone writes $\mathrm d x$.

I still don't know...

I really struggled with the $\epsilon-\delta$ definition of limits, especially for non-linear functions. This was also my first exposure to proof, as in: Prove that $$\lim_{x \to 2} (x^2 + 3) = 7$$ and I had a hard time with it at first. To be clear, computing these limits was no problem, but using the definition to prove they were correct really confused me.

At the school I was taught to look at the derivative as the instantaneous rate of change and that fit well with applications in physics. But later, when I was learning Economics in college, I had to learn to look at the derivative as the best linear (affine) approximation, and a differentiable function as a function which had 'good' linear approximations. That is also the intuition that generalizes to many variables. I wish it had been discussed in my early calculus classes.

The inverse relationship between differentiation and integration, and understanding it from the graph.

And I still have not understood that part of calculus at all! :(

I think the entire concept behind integration is hard to grasp for students who are not familiar with analysis. They tend to think of it only as the "inverse operation of derivatives", which is quite restrisctive, in my opinion.