Even as a math graduate, I still think calculus is a bit weird.
The idea of successive approximations for a slope culminating in a dy/dx term -- where we say dx (really the denominator of the limit definition) is obviously not zero, but is also smaller than any given real number. It's not clear that numbers should work like that.
Pile on that calculus courses (at least in the US) tend to care more about deriving interesting trigonometric/exponential/polynomial/whatever derivatives once using the limit definition and proceed to have students essentially memorize the derivation tricks for the remaining 90% of the course, and it can easily end up being overwhelming.
The idea of successive approximations for a slope culminating in a dy/dx term -- where we say dx (really the denominator of the limit definition) is obviously not zero, but is also smaller than any given real number. It's not clear that numbers should work like that.
Pile on that calculus courses (at least in the US) tend to care more about deriving interesting trigonometric/exponential/polynomial/whatever derivatives once using the limit definition and proceed to have students essentially memorize the derivation tricks for the remaining 90% of the course, and it can easily end up being overwhelming.