Differentiation is a process in calculus where we find the rate of change of a function with respect to its independent variable. It helps us understand how a function changes over time or space.
We differentiate functions to solve problems related to rates of change. It is also used to find the maximum or minimum values of a function, which has many real-world applications.
To differentiate a function, we use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules help us find the derivative of a function, which is the rate of change of the function.
Differentiation and integration are inverse operations. While differentiation finds the rate of change of a function, integration finds the original function from its derivative. In other words, differentiation is the process of finding the slope of a curve, while integration finds the area under the curve.
Differentiation has many applications in various fields such as physics, engineering, economics, and biology. It is used to solve optimization problems, predict the behavior of systems, and analyze the growth and decay of populations. It also helps us understand the motion of objects and the behavior of markets.