Differentiation Techniques

aggfx

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!

uman

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.

aggfx

Clearly, the point of including that rule is for the sake of a complete list.

snipez90

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 ;).

aggfx

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.

Kurdt

For those who aren't aware, Hootenanny has a good thread with a lot of the results (and more) derived in it.

http://www.physicsforums.com/showthread.php?t=139690

samuelarnold

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

QuarkCharmer

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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uman	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.

aggfx	Clearly, the point of including that rule is for the sake of a complete list.

snipez90	Differentiation Techniques 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 ;).

Kurdt Recognitions: Gold Member Science Advisor Staff Emeritus	For those who aren't aware, Hootenanny has a good thread with a lot of the results (and more) derived in it. http://www.physicsforums.com/showthread.php?t=139690

samuelarnold	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

QuarkCharmer	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.