What is a Derivative?
The derivative of a function at any point is defined as the slope of the tangent to the graph of the function at that point. It represents how a quantity changes over an infinitesimal change in another quantity.
In mathematical terms, if y = f(x), the derivative is denoted as f'(x) or dy/dx.
Explore the Derivative with Interactive Graphs
Applications of Derivatives
Derivatives are used in a wide variety of fields like physics, engineering, economics, and beyond! They're crucial for understanding motion, changing systems, and optimizing various parameters.
- Physics: Calculating velocity and acceleration.
- Economics: Finding cost and revenue functions.
- Biology: Understanding population growth rates.