This might be a better question to post to /r/askscience since I believe the field of history of mathematics is rather small, and although there are lots of very knowledgeable historians who post on here, I'm not sure if there are many mathematicians who would be better suited to answer your question.

The most common calculus notation taught today was not created by Sir Issac Newton, but by Gottfriend Wilhelm Leibniz. He was a contemporary of Newton's, and they both discovered calculus (errr... invented? Math, unlike science, is a little fuzzy in this regard) at about the same time. Newton's notation is used in physics, but isn't as common.

Math, much like science in general, evolves like a stair case, with mathematicians standing at the top and adding steps. While Newton was obviously a genius and a ton of what we know today is due to him, he had thousands of years of mathematics to stand upon.

If you took him and showed him our modern day calculus, obviously he would need some things to be explained as far as notations go, but he would understand pretty quickly.

Calculus isn't really such an obscure concept. It is honestly pretty simple and logical (the idea, not necessarily the problems.) I don't think there are many aspects whatsoever that someone with the brain power of Newton would struggle with.

As I said, its like a staircase. Take Newton and show him modern calculus, and he'd be able to walk right up to the top and start from there.

Calculus, like algebra, trig, etc, is a tool to use. There is no reason why Newton (or really any other mathematician in history) wouldn't be able to grasp calculus and learn to use it.

Source:

Multivariable Calculus by James Stewart, 6th edition

4 years of University Math and Physics classes

One of the key arguments for the purity of math is that due to the fact that there is almost always a provably right answer to a question in it (at least at the basic levels), rarely do we need to throw out or call into question the work of mathematicians, even the ancient ones, but rather build upon their traditions and expand on their theories. Calculus is no exception.

In all honesty, calculus, at least in it's most basic form taught in schools today, hasn't evolved all that much from the days of Newton and Leibniz --we still use Leibniz's notation! Interestingly enough, Newton and Leibniz came up with the concept of calculus independently of one another at almost the same time, though Newton started with differentials and Leibniz with integration. Both were working from the early tradition of Descarte and Fermat who developed some of the ideas that would later become Calculus.

In 1664 Newton began to work on fluxional Calculus with the explicit purpose of devising a mathematical language to communicate his ideas of physics. Fluxional Calculus, despite the odd name, is really just his version of Calculus and the only real difference between the Calculus he created and the Calculus in a high school textbook is the notation and the rigidity of rules.

Leibniz came at the idea from a more philosophical swing. Unlike Newton, whose work in math was part of a long period of work on physics, Leibniz took up math largely on a whim and began to work primarily on the idea of integration with special interest into the realm of infinitesimals as it was philosophically fulfilling to him.

This independent development actually led to a minor controversy over who truly "invented" Calculus. Newton's work, despite having been started earlier was not published until after Leibniz but their conclusions were largely the same. It led to a somewhat nationalistic split between the two and briefly created two schools of math.

In any case, by Leibniz's death in 1713 his and Newton's work had been combined and by the end of the 18th century had become formalized and expanded upon in minor ways. The only real major development in Standard Calculus, to my knowledge, is the work done in basic Differential Equations by Bernoulli and later Euler, and Euler's work on identities and forms, but outside of Calculus derived maths like Operation and Non-standard Calculus, applied Calculus, and things that given my limited knowledge of modern math above an undergrad level I can barely conceive, they would easily adapt to what is taught today and given that nearly all modern math and developments since their time depend upon them, they could probably catch up to speed fairly quickly.

Sources

• Calculus With Analytic Geometry 2nd Edition. Simmons, George my old Calc I and II book, how I miss you

• A Concise History of Mathematics: Fourth Revised Edition. Struik, Dirk

• A number of math classes from my stint as a math major.