A common question and some comments

I often hear students said that if we have formulae for finding derivatives, why do we need to use the limit to find the derivative at one point? Well, my answers to this are

1. the slope of the tangent line is a limiting process (from the scant line) so you need to understand why we take the limit.
2. you will be asked to find by using the ''limit'' definition. Of course, if I ask you to compute by hand, the functions would have to be simpler, such as polynomial functions of degree 1,2 or 3.