
Today Newton and Leibniz are generally considered the twin independent inventors of calculus, and they are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret. This long and bitter dispute has been swept under the carpet by historians--perhaps because it reveals Newton and Leibniz in their worst light--but this book tells the full story in narrative form for the first time, ultimately exposing how these twin mathematical giants were brilliant, proud, at times mad and, in the end, completely human.--From publisher description.
Another great book is "Infinite Powers" by Steven Strogatz (https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Univ...).
Mathematics and Its History (Undergraduate Texts in Mathematics) 3rd ed. 2010 Edition by John Stillwell
The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) by Carl B. Boyer
A History of Mathematics by Carl B. Boyer
A Concise History of Mathematics: Fourth Revised Edition (Dover Books on Mathematics)A Concise History of Mathematics: Fourth Revised Edition (Dover Books on Mathematics) by Dirk J. Struik
Introduction to the Foundations of Mathematics: Second Edition (Dover Books on Mathematics) Second Edition by Raymond L. Wilder
Mathematical Thought from Ancient to Modern Times by Morris Kline (3 volume set)
The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time by Jason Socrates Bardi
There is also a "thing" in mathematics that is sometimes called the "genetic approach" where "genetic" is roughly equivalent to "historical" or maybe "developmental". IOW, a "genetic approach" book teaches a subject by tracing the development of the subject over its history. One popular book in this mold is: The Calculus: A Genetic Approach by Otto Toeplitz