Main Question or Discussion Point
In Calculus, I am studying differentiation at the moment. The two equations is the basic Derivative function: (f(x+h)-f(x))/h and the alternative formula: (f(z)-f(x))/(z-x); and I can see how they both have their own purposes for finding the tangent line and such; but when will differentiation operators (dx/dy) ever be used practically in Calculus. Thomas' Calculus skims over it a little too quickly and doesn't flesh it out as much as I would have liked it to. Can someone help me out on how and why I would use it (compared to the other two methods) and if someone can back it up with an example, which is how I learn best, I would greatly appreciate it!