What are some helpful tips for understanding derivatives?

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    Differentiation
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Discussion Overview

The discussion revolves around tips and resources for understanding derivatives, including cheat sheets, proofs, and various rules associated with derivatives. Participants share their perspectives on the usefulness of memorization versus understanding concepts, as well as suggestions for organizing information about derivatives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant shares a cheat sheet for learning derivatives and expresses intent to add more examples and rules.
  • Another participant suggests that relying on a cheat sheet indicates a need for better conceptual understanding of derivatives.
  • A different participant defends the inclusion of basic rules in the cheat sheet for completeness.
  • One participant encourages proving the rules listed rather than just applying them, suggesting that understanding comes from working through examples.
  • A participant mentions plans to create a tutorial on derivatives and share it later.
  • Reference is made to an existing thread that contains derived results related to derivatives.
  • One participant highlights the importance of linearity in derivatives and provides an example of a polynomial function's derivative.
  • Another participant suggests that using Lagrange notation may be more visually appealing and easier to remember for those who prefer lists.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of memorization versus understanding in learning derivatives. There is no consensus on the best approach to learning or presenting derivative rules.

Contextual Notes

Some participants emphasize the importance of proofs and understanding over memorization, while others focus on the utility of cheat sheets. The discussion does not resolve the debate on the best methods for learning derivatives.

aggfx
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Hey all-

I typed up this little cheat sheet to help me with my learning of derivatives so I though someone else might want to use it for reference. I plan to add to it some examples as well as log and e rules. I will keep you updated if there is any interest in those as well.

Enjoy!
 

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If you need a cheat sheat to remember that the derivative of a constant is zero, you should work on understanding the concept of a derivative better.
 
Clearly, the point of including that rule is for the sake of a complete list.
 
Not a bad list but hopefully people can actually prove everything on there before just applying it. Admittedly after working a decent number of examples, nothing really needs to be memorized. Also I would put the "extended power rule" after the chain rule ;).
 
That may be a good thing to show (the proofs). I plan to build a little tutorial on derivs. I will post it when I am done.
 
Maybe the easiest and most useful formulas are the ones that say that the derivative is linear:
(f + g)'(a) = f'(a) + g'(a)\\ (cf)'(a) = c f'(a)

Combined with the formula (xn)' = n xn-1, we see that every polynomial function has a derivative at any point.

Example. For P(x) = 1-2x + 3x4 -5 x6, we have
P'(x) = -2 + 12 x^3 - 30 x^5
 
This may be a bit picky, but if your the type who likes lists (like in the original post), you might find it much easier to remember (and nicer to look at) writing them in Lagrange notation.
 

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