Trig. Identities & Their Derivatives

[NSX]

I'm just wondering how you guys remember these derivatives;

 

I mean, d[sec(x)]/dx = sec(x) tan(x) isn't as easy to remember as d[sin(x)]/dx

 

 

So yeah, do you guys remember the tan & inverse trig derivatives just as formulaes? Or you use them so much that you it's already in your head? Or...any strategies?

[VendingMenace]

well...i dont remember them any more and i doubt that people who don't use them everyday do either. If you are trying to memorize them for a class, then try brute memorization, just shove 'em into the old short term memory before the test. (my advice, worked for me! lol)

 

It is my experience that anything that is worthwhile having memorized for what you are doing you will already have memorized. that is, anything that would save you enough time by having memorized, you probably use enough to have already have it memorized. It is not really worth memorizing things that you can just look up in a book or on the web. Of course this is just my two cents....and i hate memorizing things (preaps i am just lazy).

 

Of course, if you are just memorizing things for the fun of it (::shudder: then by all means, have fun! If not, then don't worry about it. If it somthing that you should have memorized for a job you will have it memorized in due time. If it is something for a class, then cram it into short term and go do something worthwhile with your time (like play frisbee)

 

Anywyas, best of luck!

[scm007]

Hmm I never had trouble memorizing them, or there inverses

 

If your having problems just write them in terms of cosine and sine, you could be able to derive them with quotient/product rules.

 

For example d/dx (sec x) = d/dx (cosx)^-1 = (sinx)/(cos x)^2 = tanx * secx

 

See? And for inverses, just do it in terms of y, like if y = arcsin x, then x=siny

 

Drawing a triangle you should be able to figure it out from there.

[Guest Tashi]

well...i dont remember them any more and i doubt that people who don't use them everyday do either.

 

So not true!

 

I remember

 

d[sec(x)]/dx = sec(x) tan(x)

 

by thinking of sec as a bottle of sec wine, and tan as a tin of tan coloured varnish. I imagine this one as a bottle of wine (sec) swinging and smashing into another bottle of wine (sec), which it smashes, then hitting a tin of tan varnish (tan) which in turn smashes the original wine bottle.

 

I store this sequence on an imaginary furry flag which i call "standard differentials" (i.e. flag=standard, furry=de-fur-entials plus I like rabbits and other furry things) and all my standard integration formulae are stored on an imaginary flag striped with burn marks (it has been grilled -- inte-grill ~ integral -- geddit?).

 

It is easy to think of the silly symbols and sequences, concentrating on the visualisation is the hard bit, but this really is where EFFORT is exteremly important, time investment is not. You have to review it a lot initially like a mental video clip, making it faster and faster in your mind with each review; after that it is extremely easy to recall, even years later, and well worth the effort. It shouldn't take more than 10mins to memorise each one, but only do a few at a time or a day, concentrating deeply is tiring

[bloodhound]

I think that with enough practice, most of the standard differentials and integrals will be stored into ur brain. just like writing, or multiplying simple number, or walking, its gonna be natural.

 

Loads of Practice is what i would recommend.