Derivatives are mathematical concepts that represent the rate of change of a function at a specific point. In other words, they show how much a function is changing at a particular point.
Derivatives are used in science to model and analyze physical phenomena. They are particularly useful in physics, engineering, and economics to understand how quantities change over time or in relation to other variables.
The derivative of a function at a given point is equal to the slope of the tangent line to the graph of that function at that point. In other words, the derivative is the rate of change of the function at that specific point.
Derivatives can be calculated using various methods, such as the limit definition, power rule, product rule, quotient rule, and chain rule. These methods involve manipulating the original function to find the derivative function.
Yes, derivatives can be negative. A negative derivative indicates that the function is decreasing at that point, while a positive derivative indicates that the function is increasing at that point.