Derivative Rules: Power Rule, Additivity, and Scalar Multiplication

We look at three rules that combined let us take the derivatives of polynomials: The power rule (for x^n), additivity (the derivative of a sum is the sum of the two derivatives) and scalar multiplication (the derivative of a scalar multiplication is the scalar multiplication of the derivative). We try to prove or geometrically justify the latter two.
Learning Objectives:
1) Compute the derivative of a polynomial
2) State the power rule, additivity of derivatives, and scalar multiplication of derivatives.
3) Use the definition of the derivative to prove derviative laws.
Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.
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[@juliannafotheringham7101]

amazing as always

[@ranaraghuverndrapratap]

Very nice concept

[@lewistomalin1008]

the best

[@まつまつ-x1f]

Nice!