Derivative formulas through geometry | Chapter 3, Essence of calculus
A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition. Check out Brilliant: https://brilliant.org/3b1b ...
==========
Now that we've seen what a derivative means, and what it has to do with rates of change. Our next step is to learn how to actually compute these guys, as in if I give you some kind of function with an explicit formula you'd want to be able to find what the formula for its derivative is. Maybe it's obvious, but I think it's worth stating explicitly why this is an important thing to be able to do. Why much of a calculus students time ends up going towards grappling with derivatives of abstract functions rather than thinking about concrete rate of change problems, Is because a lot of real-world phenomena. The sort of things that we want to use calculus to analyze are modeled using polynomials, trigonometric functions, exponential's and other pure functions like that...
==========
Now that we've seen what a derivative means, and what it has to do with rates of change. Our next step is to learn how to actually compute these guys, as in if I give you some kind of function with an explicit formula you'd want to be able to find what the formula for its derivative is. Maybe it's obvious, but I think it's worth stating explicitly why this is an important thing to be able to do. Why much of a calculus students time ends up going towards grappling with derivatives of abstract functions rather than thinking about concrete rate of change problems, Is because a lot of real-world phenomena. The sort of things that we want to use calculus to analyze are modeled using polynomials, trigonometric functions, exponential's and other pure functions like that...
