Two problems that mathematicians were facing led to the discovery of differential calculus:
(1) how to define the instantaneous velocity, acceleration, and rates of change;
(2) how to construct the tangent line to a given curve at a point.
In this chapter, we will start with these two problems to develop the concept of a derivative and show what it means geometrically. Then we will learn how to find the derivatives of various functions. In more detail, we will cover: