If you generally are excited about why things happen then you may like university mathematics. By "things happens", yes the differentiating example above it true, however there are other parts of mathematics. Can we categorise knots (a knot: take a piece of string, make a knot, then tie the ends together)? Can we be sure our integration from -N to N converges to the int from -infty to infty if we send N to infty? (e.g. Fourier transform). Why is it that matrices are a natural way to express things? (Presentation theory).
However you need more than just excitement. To enjoy maths you will need to understand that the first 2yrs are a slog. There is SO much to learn because of the way it is taught at A level. Expect to work 9-9 weekdays, 10-4 weekends. And U will get upset by this as ur non-maths friends will do a fraction of that work. And at the end, ur maths degree is as employable as a econ degree, but u did twice the work load.
Ull also have to understand uni is aobut learning urself. Get some books, get reading, get exploring, do examples, and a think. U do not get spoon fed like at a-lvl.
Jx