In any regular calculus or real analysis course, we learn the definition of the derivative of a function $f(x)$ as $$f^\prime (x)=\lim\limits_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h}$$ However while studying abstract algebra we come to know that differentiation is just like any operation (like addition, multiplication etc.) but on functions. So I want to know that is there a way to define an algebraic structure with the underlying set as the set of all differentiable functions and the operation of differentiation.
And also if it's possible to define differentiation in such a manner, how to connect it with the analytical definition of differentiation.
from Hot Weekly Questions - Mathematics Stack Exchange
Soham Sarkar
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