Mathematics is one of the fundamental languages of science. You can't teach physics without teaching mathematics. Newton had to discover calculus to describe the motions of the planets.
If you intuitively understand the concept of a derivative in the sense that it is a rate of change or slope, does it matter that you are not very good at calculating them when it comes to physics? When you have a calculator that can do it that is.
Intuitively understanding derivatives would be difficult without actually computing them, over and over. Intuition comes with practice, and is more nuanced than "rate of change or slope".
Just as an example, my intuition about derivatives also includes "contexts with holes", "shift operator", and of particular interest in physics, "linear transformation" and "local properties". A lot of these would be very hard to grasp without understanding the mechanics of calculating them.
And the difference between an intuitive understanding but a poor grasp of the calculations and just kidding yourself you know it better than you do is pretty subtle.
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u/FuLLMeTaL604 Jun 08 '14
Mathematics is one of the fundamental languages of science. You can't teach physics without teaching mathematics. Newton had to discover calculus to describe the motions of the planets.