The derivative of a function represents the rate of change of that function at a specific point. It measures how much the output of the function changes when the input is changed by a small amount.
The derivative of a function is calculated using the limit definition of a derivative, which involves taking the limit of the change in the function's output divided by the change in the function's input as the change in input approaches zero.
The derivative of a function tells us the slope of the tangent line to the function at a specific point. It also tells us the direction and rate of change of the function at that point.
The derivative of a function is important because it allows us to understand how a function changes over time or in response to different inputs. It is also essential in many areas of mathematics, physics, and engineering.
The derivative of a function is a completely new function that describes the rate of change of the original function. It is related to the original function through a set of rules, such as the power rule, product rule, and chain rule, which allow us to easily find the derivative of more complex functions.