I don't think you need to go to higher level math to run into this sort of problem. When we're in school solving equations, getting to the initial stages of ca

I don't think you need to go to higher level math to run into this sort of problem. When we're in school solving equations, getting to the initial stages of calculus, you start running into identities like sin^2(x) + cos^2(x) = 1, which sometimes but not often are written with three parallel lines instead of two. What this means is that the functions on either side of the sign are equivalent, any x you pick doesn't change the graph. At some point, you will be solving simultaneous equations, and someone will have the bright idea that you can just differentiate both sides and just solve that. This happens to be true if you have something like above, it's still valid that the derivative anywhere is the same, since they are the same function. But if you are actually just finding the crossing point of two graphs, like one normally does at that level, then the equality is only for a particular value of x, and there's no reason the derivative would be the same. In general there's a lot of these little notation things that creep up around that stage. The big one is treating dy/dx like a fraction, which you can do in certain cases to solve differential equations, but only in certain cases. If you don't understand why, you might get very confused about what the symbols actually mean.