Inverse Trigonometric Functions - Derivatives

[BaconSizzle48]

@ajajajaj85, it'd be the same as taking the derivative of 2x. The 2 is the constant and the x drops off. See power rule

[shawnxcruz]

I am curious as to why you took the derivative of (√(2t-1))^2? If this were so then wouldn't taking the derivative of arccosine of t be equal to -2/(√(1-t^2))? Please respond because this is driving me crazy

[ajajajaj85]

why is the derivative of 1/a*x equal to 1/a?

[ANILTHEGAME]

Your explanations is way better than any Calculus teacher on earth =)

[patrickJMT]

@ANILTHEGAME glad you like 'em

[solidiquis1]

Hey JMT, you should adopt me.

[Sakura162]

You can take the place of my Calculus teacher any day!

[707Cookiez]

When I look up math help on Youtube, I sigh a breath of relief when I see your videos come up. :'D

[patrickJMT]

@707Cookiez ha, i am glad you feel that way : )

[lillibeth13]

@patrickJMT Hey Patrick, my calculus professor says it's incorrect to say that by squaring a square root you get the stuff inside the square root. He says that it SHOULD be the absolute value of whatever it is you're squaring. Is that true?

[patrickJMT]

@lillibeth13 yes, he is correct

[vince48910]

@707Cookiez not only that but I search PatrickJMT next to the lesson :)

[patrickJMT]

@vince48910 also a very good idea! : )

[nextblain]

hey patrick can u do a video of integrals of inverse trig functions? not using them but ingrals of them? like integral of arc sine n others? i m confused on wikipedia :S

[patrickJMT]

@nextblain i already have

[Soccerjunky04]

Patrick I cant find any examples of anti-derivatives using inverse trig functions:(

[patrickJMT]

@Soccerjunky04 if you type ' inverse trig ' in the search box near my list of videos, some stuff will pop up

[Soccerjunky04]

@patrickJMT Thanks!



[patrickJMT]

@ARQ911 rarely; they are all in the textbook already.

[tshgllm]

Thanks, I find your videos really helpful! It was easier to follow along in the videos when you wrote on paper in sharpie insted of the dry erase because you weren't erasing the steps. Please do more videos that way. :)

[dcocky1]

Hey Patrick I'm having problems with this question arctangent(tangent3pie/4) find the exact value of the expression

[Reggaemom67]

@dcocky1 The answer is -pi/2(or -45degrees)

[Reggaemom67]

@dcocky1 The answer is -pi/2(or -45degrees).

[gabby19g]

Your video is VERY helpful compare to most of the videos I have watched. Thank you so much!

[RanyaI12]

I don;t understand what you did for the second equation i know is the chain rule so I thought the answer would be -1/sqrt(1-x^2) *sqrt(2t-1) *(1/2(2t-1)^-(1/2)

[catherinekirby1]

Your videos are the first resource I jump to when in need of help for calculus. THANK YOU.

[AdolfHitlerVEVO]

THUMB UP SO EVERYONE SEES!

heres equations in case if your confused: G[F(X)]

chain: G'[F(X)]mutiplayF'(X)  (LOL cant find the mutiply sigh)

u should be luck ur only seeing basic derivitive rules, cuz intgral rule is confuseing as hell

[pennjersey83]

At 5:20 When taking derivatives of the LN aren't you suppose to multiply by the inside?

[7abeb0al0mostafa]

why isnt there patrick JMT

for every thing?

[bennyvakathanam]

thanks a lot it`s very helpful.

[tmlrlz]

Did you make any videos for the derivative of trig functions. Like questions that involve how derivatives of trig. the derivative of sin is cos and for cos is -sin.

[knotnyce]

in example 2 a thought we should differentiate arc cos of the thing in the bracket "THEN PUT BACK WHATS IN THE BRACKET"... & then we multiply by the derivative of whats in the bracket??? O.o

[WTVBqdemon]

trigonometry annoys me.

[drionshk]

At 5:38 when you get x^2 over a^2...

How come you then don't have to then multiply by the derivative of that? It's a *constant-times-variable*, so shouldn't you multiply by *constant* on the outside of that fraction?

[oshomegie]

Good Job ... Thanks

[idrinktoomuchcoke]

hi, thank you for the videos.

Could you also do a video on derivatives of trig functions? e.g. smthing like f(x)=cos(10^(7x))?

[jackxzx]

hey patrick thank you alot for the video, theres one thing i don't get tho..

in the third example, you differntiated Ln(x-a)-Ln(x+a), which is equal to 1/(x-a) - 1/(x+a), didnt you say "a" is constant and remains the same?

then izent it suppose to be 1/(x+a) * a ?

we are suppose to differntiate whats inside the bracket izent it?

[patrickJMT]

@jackxzx yes, but the derivative of (x - a) is 1 - 0 and the derivative of ( x + a ) is 1 + 0, so you are only multiplying by 1 in both cases (the a term goes away after differentiating since it is a constant)

[jackxzx]

@patrickJMT thank you professor patrick you the best.

i nailed my test today thanx to you

thnx a bunch!

[walkerwiggins0]

when your showing the formulas for csc and sec, my calculus book says the first x on the bottom of the funciton should be a absolute value.

[5857612]

on the last problem you could of factor out 1/2 from the second part right?

[5857612]

on the last problem you could of factor out 1/2 from the second part right?

[letthemxeatcake]

Was multiplying the numerator by a supposed to cancel out the a^2 in the denominator?

[blackberry8319]

i think you just saved my life

[bullseye1224]

thank you so much! once again, another helpful video :)

[defendurrootz]

wouldntt you have to times everything by 'a' Not just the first fraction???

[JoshuaTaylor1992]

for the derivatives of csc(x)^-1 and sec(x)^-1 the x on the denominator should be an absolute value

[halfblond99]

sexy handwriting ;)

[DBR1308]

@patrickJMT Horse talk I say!

[yonlyonem]

@patrickJMT very cute. & yea i wouldn't have hope of passing if it wasn't for your videos

[unclefroggyiscool]

thanks alto

it helped a ton!!!

[ConfusionPixie2]

i think you forgot to put -1/2 in the tan ln equation....

[lynncarmen]

you should do a video on just plain derivatives of inverse functions (like calculate g(b) and g'(b) where g is the inverse of f)

[lynncarmen]

aw man, hes married :(

[calliefla]

@lynncarmen creepy

[LoGrella]

your videos are extremely helpful. i really appreciate the time you put into these examples. thanks so much, these videos are a great supplement to my class :)

[Machammerballs]

How do you derive inverse csc, and inverse sec using a reference triangle. I can do it with the regular functions but when I try with with these two it turns into an exercise in pain and frustration.

[xxcoldsteelexx]

when you took the ln for the parentheses part in the derivative of the tangent function problem, why do you not multiply the natural logged parentheses with the derivative of the inside after making it 1/x of itself and before distributing 1/2?

[mariomaruf]

That's page 371-ish of my book.

[1matth3w1]

Respond to this video... do you have videos explaining how to take derivitives of trig functions? cause i dont understand how sin-1 became 1-x2.. where did the ^2 come from?

[MattMcq99]

squeeeeeeeer

[patrickJMT]

@MattMcq99 that is a kentucky accent for you.

[Altare1994]

@patrickJMT WOOOO KENTUCKY!

[patrickJMT]

@Altare1994 i need to get back and visit soon!

[Mastodon1432]

@MattMcq99 way to make to the top comments matty boy

[bundeligafan]

you rock

[SirStrum]

Hey Patrick, just wanted to say that these videos really help... Sometimes, some professors arent so great with explaining this stuff, and I always come back to your videos. Thanks a bunch!

[eoterm]

Hey if it is not to much trouble could you make a video where you derive the inverse trig functions with that formula

(f^-1)'(b) = 1 / (f"(f^-1(b)))

my professor was doing it where you drew a triangle and one leg was 1 the other leg x and the hyp was something like sqrt (1-x^2)

not sure what he was doing

thanks

[brianh827]

I really appreciate your videos and way of teaching the calculus without trying to confuse anyone

[patrickJMT]

@brianh827 ha, well, i dont think anyone intentionally tries to confuse while teaching...

[sistagoldenhair9]

@patrickJMT haha... no, I'm pretty sure my professor tries to confuse us while teaching... aaaand mission accomplished, because I have no idea what he's saying. So thanks for these videos, because I'm not sure I could pass the class without them!

[TwistedLemniscate]

I moarn the day that I finish all of your Calculus videos. Like someone else already said, "these are better than porn." They really are.

[MattMcq99]

@TwistedLemniscate not true at all....

[onetimeuse12]

your videos rock!

really good

[Darian458k]

this question WOUL require you to TAKE a common denominator and rationalize and recognize the difference of sums twice...the answer is[3*(a^3)+a(x^2)] / [a^4-x^4]

[McBeefsupreme]

nvm got it :P 2xtan^-1x

[McBeefsupreme]

whats the derivative of (1+x^2)tan^-1x-x just give me a hint if possible

[arkomanis123]

damn it reminds me last year on high school but i have completely forgotten all i have learned :o

[caorr]

thanks :) u rly helped

[lessavyfav712712]

Brilliant.

[imadElghourani]

your a bitch

[TengoNoNombre]

cause he is a shemale

[totlolrofl]

AnimeAccount1

[CWATTAGE]

stupid

[ianharwood]

i write neater than him and i assure you i have a dick

[shamoono]

hha im left handed too!! hi5

anyway nice video

[kelvinella]

you can simplify it down to 2ax^2 / (x^4-a^4)

[aegisforex]

Can you make a vid where you prove the derivative of inverse trig functions? Only arctan, arcsin, and arcsec would be necessary.

I think it may be easier to derive them rather than memorize them when needed, but I seem to get lost in the process.

Thank you.

[salgadoxx]

im left handed too!!!

[hellowsaw]

Hi there do u happen to have derivatives of trigo functions. i mean just derivatives of trigo not inverse function of trigo.

[Dheart8D]

u r left handed(: haha .

[jayr64]

maybe im generalizing, but i would like to thank you on behalf of ALL first year university calculus students.

[xDirectJABx]

ha... agreed

[TedKong101]

or high school seniors taking AP Calc :D

[jonnie3424]

or Ib Calc

[fragm3nted]

yeah obv.. u have to dial that in your phone and ask the guy for the answer....

[ThirtyYearsWar]

when i use the inverse cosine button on my calculator, it always gives me the same answer: .463647609

[vitaminEATER]

Legit.

[mackeny1]

this dude is ill... helpful video's bro

[AdolfHitlerVEVO]

@mackeny1 the dude is "ill"??

[mackeny1]

@AdolfHitlerVEVO means he's really good...keep up

[AdolfHitlerVEVO]

@mackeny1 cant keep up, i died in 1945

[eldemixqui]

look at the unit circle

[begolag2]

derp derp derp

[Sophf]

That's radian measure, which is a replacement for the degree measure that you learn earlier on in trigonometry.

180degress = pi, so pi/6 would be 30degrees.

[HANNONKEVINP]

Why don't you take the derivative of the x-a after ln(1/(x-a))

[kikbalkid]

Do you have a video on problems for the derivatives of regular trigonometric functions? I always look up your videos the day before I take an exam and I have an A in Calc 2 :) My test is on Friday though. Hopefully you can link me the right direction.

[JMRCProductions]

what o.O I have to learn this if I'm going to be a game programmer?! (at least what a site i visited said)

It seems impossible

[olyphant07]

.....

[patrickJMT]

you said it

[Tyme1v1aster]

I've always wondered why my calc book never uses Arccos, but uses Arcsin and Arctan. Good to see you included Arccos lol.

[xxxmagixxx]

You are my savior.

[DeJayHank]

i think the last equation can be simplified to [2a(x^2)] / [(x^4) - (a^4)]

but whatever :P

[Cam50000]

yeah i just got that too

[Telaco]

hey! your a lefty too! : )

[princessjennyy143]

this is called calculus in the US? o m g! then why am i doing this? im not even in calculus! : (

[mrgatorland]

because taking derivatives is calculus. Sometimes they teach students the derivative identities in lower classes just to give them an intro to it.

[ronzam2002]

good job! I understand your examples!

[patrickJMT]

excellente!

[marijo790]

hey, I'm having a hard time understanding the whole inverse functions... are only Trigonometric?? Can you explain a simple inverse function, no trig involved?

[christopherchubb]

any inverse function is just the oposite, usually denoted by a little -1 like how he has shown. Any inverse function cancels out the original, for example log and e^ are inverses because log(e^x)=x, they cancel. similarly arcsin(sin(x))=x. Note: inverse trig functions can be called arc instead(easier to type :P). They aren't usually used much outside of trig functions and logarithms

[Vondutch01]

Have you any videos of exponential trig derivatives?

Its not clear to me what to do because my problem has e raised to sec of 3 theta.

[bryagha]

Thanks!

[TrickyNekro]

That was a nice one...

I always tend to forget inverse trig derivatives and integrals...

Although arctan is the easiest to remember...

You know I have a test on maths tomorrow have anything quick to propose to remember these thingies???

[metalmaiden90]

is there a video showing some of the proofs of these inverse trig derivatives?

[patrickJMT]

none by me, but they are not hard to derive. any calculus text should give the justification too

[polizorian]

Hello !

At what age do you study this kind of calculus ?

[amanwithamission]

Nice AP Calc review. Good stuff.

[renbaker1]

these videos are very helpful!! Thanks:)

[joojoo00oo]

the way u explain it its like its easy :-s thanx for making me feel better!

[sean2339]

So what is the best way to learn calc without doing homework?

[patrickJMT]

figure out how to install a microchip in your brain that will relay calculus info would be a good way

[javarie19]

He's right...theres no way you'll be able to do it without doing h.w....we do need chips installed to make this way easier..

[tiNtiN11]

Thanks for taking the time to put this up, really helpful. Had no clue you had to get the derivative beside the arc___(x). :)

[cubencis]

are we expected to memorize the derivatives of inverse trig functions or should i expect them provided?

[patrickJMT]

i would assume most teachers would have you memorize them!

[born2race17]

Yeah, my AP Calc teacher gave us a separate quiz on what the derivatives of the inverse trig functions were. So it would help in the long run to just memorize them.

[jenloesem]

would the 1's cancel when you have square root of 1-(2t-1)?  that should be equal to

1-2t+1 and the 1's cancel so it'll be -2t

right?

[ozakigw]

if u have 1 -2t +1

you have (1+1)-2t

hence 2-2t

[patrickJMT]

thanks for helping!

[jenloesem]

yeah you right ,,, sorry for some reason i though the first 1 had a negative sign :-)

thanks

[ozakigw]

no worries

glad to help

[patrickJMT]

ozakigw is correct!

[jachina]

If you have free time, please do another video on Inverse Trigonometric Functions, a harder example if possible, Thank you!

[patrickJMT]

just a harder derivative example?? i can do that!

[Aerex12]

@slayerxxchick3: The derviative of the inverse sine is 1 / sqrt(1 - u^2) and u is a function respect to x. So lets say you had sin-1(2x) then it would be 1 / sqrt(1 - (2x)^ 2 * 2. You have to chain rule the function of u as well in this case the derivative of 2x is 2. Hope that explained it.

[slayerxxxchick3]

Btw, I understand the arcsin x/ inverse of sin, and whatnot. I just don't understand why you just don't take the derivative of sine

[slayerxxxchick3]

why do you make the derivative of the sin a square root of 1-(x squared)?

My showed us a different way.

You take the negative 1 out, bring it to the front, replace the -1 with a -2, change sinx to cosx. Then bring it to the bottom, making the -2 a +2.

I don't understand why to did it like that.

Could you explain?

[raidenms]

could you do some lesson about the classic fourier function?

[Waranle]

Thank you alot Patrick, having looking for these inverse functions and their derivates