If ##y=x^2##, then 2x is the instantaneous rate of change of y at x.jasonlr82794 said:Yeah, I know, but what does the y have to do with the 2x?
At any point x, the slope of the y=x2 curve is known and is equal to 2x.jasonlr82794 said:Yeah, I know, but what does the y have to do with the 2x?
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is often used to describe the slope of a curve or the instantaneous rate of change.
Some other ways of expressing a derivative include using the notation "dy/dx", "f'(x)", or "df(x)/dx". These notations all represent the same concept of the derivative.
A derivative can be calculated using the limit definition, which involves taking the limit of the difference quotient as the change in the independent variable approaches zero. Alternatively, derivatives can be calculated using differentiation rules and formulas.
A derivative represents the rate of change of a function, while an antiderivative represents the original function before differentiation. Essentially, an antiderivative is the inverse operation of differentiation.
Derivatives have many practical applications in fields such as physics, engineering, economics, and more. They are used to model and analyze rates of change, optimize functions, and make predictions in various real-life scenarios.