Differentiation is a mathematical process used to find the rate of change of a function with respect to its independent variable. It involves finding the derivative of a function at a specific point.
Differentiation is important because it allows us to analyze and understand the behavior of a function. It is used in many fields such as physics, economics, and engineering to model and solve real-world problems.
The basic rules of differentiation include the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivatives of functions with various combinations of operations.
Differentiation and integration are inverse operations of each other. Differentiation finds the slope of a function at a specific point, while integration finds the area under the curve of a function. Integration is the reverse process of differentiation.
Differentiation is used in many real-life applications such as determining the velocity and acceleration of moving objects, optimizing production processes in business, and predicting financial market trends. It is also used in medical imaging to analyze and interpret data from scans.