4.1 Interpreting the Meaning of the Derivative in Context

While we use the word derivative in calculus, it is important to know that we are just talking about the slope at a point! In real-world situations, there are different ways that the idea of a derivative can be interpreted to us. 

Whenever we talk about a rate of change, we are talking about a derivative. A very popular way to represent derivatives is talking about measurement with respect to time. Like, meters per second, miles per hour, liters per minute. 

If you are looking at a rate that is something like feet per second squared, you are looking at a second derivative!

When we learn implicit differentiation, it is often in terms of x and y. We take the derivative with respect to x, d/dx of some equation, and when we are taking the derivative of a y term with respect to x, we need to apply chain rule, knowing that the derivative of y with respect to x is dy/dx.