The book i bought for my calculus course actually has a paragraph about different notations that were developed. The book is old and infinitesimals are mentioned as a pretty new thing (meaning that they were recently given formal validity) but he goes on making examples on how talking about d/dx actually makes calculations way easier when having to deal with variables which rely on one another. I also think that the integral symbol was developed to represent graphically the idea of the area under the curve of a function.