What is differential calculus? Let’s take a car trip and find out!
Suppose you take a trip from Dhanmondi to DSC. That’s roughly 26km, and (depending on the traffic), it will take about two hours. Now, we all know that distance equals the rate multiplied by time, or d = rt. In this example, we have distance and time, and we interpret velocity (or speed) as a rate of change. So you could figure out your average velocity during the trip by dividing distance over time. That is: (26 km) / (2 hours) = 13 km/hour
However, you know that when you’re in Dhaka city, you’re driving much slower than 25 km/hour! On the other hand, when you get to the highways, it may be 80 km/hour. The calculation was just an average, and it’s answering the question: if my velocity stayed the same throughout the entire trip, what would it be? But your car knows better. It has a speedometer that keeps track of the speed (velocity) at any given instant. When you look at the speedometer and it reads 50 km/hour, which tells you the instantaneous velocity at the particular instant of time you decided to look at it. How does it know? Your car is doing something like differential calculus to figure it out!
Differential calculus is a method that deals with the rate of change of one quantity with respect to another. The rate of change of x with respect to y is expressed
Also, the derivative is simply called a slope. It measures the steepness of the graph of a function. It defines the ratio of the change in the value of a function to the change in the independent variable.
Why do we use differential calculus?
You may have a look at the –