Differentiation is a mathematical process of finding the rate of change or slope of a function at a specific point. It involves calculating the derivative of a function, which represents the slope of the tangent line at that point.
Differentiation is important because it allows us to understand how a function is changing at a specific point. It has many real-world applications, such as in physics, economics, and engineering, where it is used to analyze rates of change and optimize systems.
The most commonly used methods of differentiation are the power rule, product rule, quotient rule, and chain rule. Other methods include implicit differentiation, logarithmic differentiation, and parametric differentiation.
Differentiation is the process of finding the slope of a function, while integration is the process of finding the area under a curve. In other words, differentiation tells us how a function is changing, while integration tells us the total amount of change over a given interval.
Differentiation has many real-life applications, such as in physics to calculate velocity and acceleration, in economics to maximize profits and minimize costs, and in engineering to optimize designs and predict system behavior. It is also used in data analysis and machine learning to identify patterns and make predictions.