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I also studied chemical engineering, and throughout high school and university that was exactly it. Calculus was a kind of magic, and you just had to learn all the spells.
With this book I finally understood why the derivative of x^2 is 2x.
Ok I’m no mathematician but I’ll still can’t see why d(x^2) = 2x.
This exact explanation is in the book: https://calculusmadeeasy.org/4.html
I tried to figure it out myself back in high school but the best I came up with is X^2 -->2x because it just fucking does.
https://www.calculusmadeeasy.org/4.html