how I remember all the trig and inverse trig derivatives

Рет қаралды 52,772

Күн бұрын

My tips for remembering the derivatives of trig functions & inverse trig functions. These are must-knows in Calculus 1 and AP Calculus AB. The main idea is to organize the functions in order so we can see a pattern more easily. Also doing lots of practice would help. Feel free to comment on your own way of remembering these derivatives in the comment section.
0:00 Derivatives for regular trig functions
3:18 Derivatives for inverse trig functions
5:22 The trig identities behind 1-x^2, 1+x^2 and x^2-1
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#calculus #math #bprpcalculus

Пікірлер: 68

@arimermelstein9167 2 жыл бұрын

I memorize only derivative of arcsin and arctan because they come up a lot. If you asked me to find any of the other ones, I would just reprove it with implicit differentiation. Also, I don’t really like the identity way. When I have to go back from the theta world to the x world, I draw a right triangle to find the relationships.

@bprpcalculusbasics 2 жыл бұрын

Yea same here. And the students say they don’t like the triangle until they see all the identities.

@user-ex1hp8ph3p Жыл бұрын

@@bprpcalculusbasicsWhy don't you call them arcsin, arccos, arctan, arccot, arcsec, arccsc? It's more easy, not?

@sorindyy8622 8 ай бұрын

@@user-ex1hp8ph3pnot really , when you use the cos^-1(x) it’s easier cus u just need to add the negative exponent

@liamwelsh5565 2 жыл бұрын

The way my calc teacher showed us to remember it is using the letters SST. If you want the derivitive of sec, it's sec x tan x. S = S * T. For tan its sec x sec x. T = S * S. For CSC and COT, you do the exact same thing but just add the C and of course the negative. And for sin and cos, they're just opposites with cos being negative of course.

@ganeshpatwal6555 2 жыл бұрын

You will definitely be useful to me next year. In 11th grade. :D

@bereket7846 Жыл бұрын

Believe me...not just useful he will be a tool

@surajjani4868 2 жыл бұрын

You are great!!

@asdf945 5 ай бұрын

Man you are the best, I have been having a hard time memorizing these but this just made it so much easier. Thank you so much from all of the struggling calculus students out there!

@Kcite Жыл бұрын

what an absolute legend, i was just struggling to remember these derivatives and saw this video. huge thanks for saving my grades!

@bprpcalculusbasics Жыл бұрын

Glad to help. Best wishes to you 😃

@sarmadmaqsood727 2 жыл бұрын

Thanks so much! really appreciated it

@nkyxd5698 2 жыл бұрын

Great video!!!!! It's so helpful for a cal 1 student like me😎😎

@curtpiazza1688 Жыл бұрын

WOW!! Great lesson! 😊

@kevinpari9500 3 ай бұрын

so helpful thank you!!

@bruceu526 2 жыл бұрын

Thank you so much, this is going to save my ass from failing my calc 1 midterms next week. Could you do hyperbolic functions and their inverses derivatives?

@xxruyle 2 жыл бұрын

I c baj

@___aaron.m7930 Жыл бұрын

great video! the most useful to me was tan and sec are best friends same with cot csc

@BAC-lc5oc 2 жыл бұрын

You are great!! thanks bro bprp

@Easylearning-cs3ji 2 ай бұрын

thank you

@alishbakhan 2 жыл бұрын

This helps alot💜

@colinhenslee2143 18 күн бұрын

I LOVE YOU

@krishjain7177 Жыл бұрын

Good COntent really helped me fr

@Jalina69 Ай бұрын

That is awesome act

@harekrishnaparhi7943 2 жыл бұрын

Gr8 video man

@lailaalabry Жыл бұрын

Thank you !!!!

@heliocentric1756 2 жыл бұрын

How I remember all the trig and inverse trig derivatives? just calculus: Video 7:15 long. FAST!: "Don't forget them"

@bprpcalculusbasics 2 жыл бұрын

😂

@hablejannat 2 жыл бұрын

Thank you sir

@zaynbashtash 2 жыл бұрын

A real hero

@stantackett107 Жыл бұрын

I must be showing my age. I was about to ask you for hints on how to define inverse cosine and cosine, because I'm reverting to my Amiga 500 using BASIC. then I suddenly remembered e^ix and it all came back. I'm 54, have degrees in math, computer science and nuclear engineering b I think it's time to retire if I can't remember simple math 😂 And I adore your channel. Like to refresh my skills watching you whoever possible. keep up the good work!!

@itsohaya4096 Жыл бұрын

Me forgetting basic arithmetic as a calc student

@suyashsahu6505 2 жыл бұрын

Lovely.

@anshumanagrawal346 2 жыл бұрын

I used to have ways to remember, but now with so much practice they are literally set in my brain like stone

@Sanwichgamingtr 2 жыл бұрын

this video is underrated

@justabunga1 2 жыл бұрын

We know that the derivatives of arccos(x), arccsc(x), and arccot(x) are negative versions of the derivatives of arcsin(x), arcsec(x), and arctan(x) (most likely used). The difference from there is that they are all off by the constant of pi/2. Adding a constant will have the derivative to be 0. Therefore, anytime the constant is off, the function always has the same derivative. You can try to integrate and see the difference from there.

@johnnolen8338 6 ай бұрын

I remember the trig derivatives by repetition. (If you do something 10 000 times, you're bound to remember it.) Also you can get the derivatives of sine and cosine simultaneously by differentiating Euler's formula. d[cos(x)]/dx = Re {d[e^(ix)]/dx} and d[sin(x)]/dx = Im {d[e^(ix)/dx}. To figure out the derivatives of the inverse functions I use a reference triangle and the inverse function theorem together. The reason for the absolute value in the derivative of arcsec(x) is because in order for arcsec(x) to be a function it has to be one - to - one. And if sec(y) = x then cos(y) = 1/x. If we differentiate this expression, we get - sin(y)·dy/dx = - 1/x^2. This implies dy/dx = 1/(x^2·sin(y)) = 1/(x^2·sqrt[1 - 1/x^2]) = 1/(|x|·sqrt[x^2 - 1]). ◼

@leonardobarrera2816 11 ай бұрын

cool!

@justabunga1 2 жыл бұрын

For the derivatives of arcsec(x) and arccsc(x), shouldn't there be an absolute value around the x (i.e. 1/(|x|sqrt(x^2-1)) and -1/(|x|sqrt(x^2-1)))? I saw those in most of the textbooks.

@bprpcalculusbasics 2 жыл бұрын

Oh yea it depends on the domain where they define the sec^-1. See 5:01

@GSHAPIROY 2 жыл бұрын

When you differentiate arcsec(x) and arccsc(x), those functions are not continuous, so you have to split them on the intervals (-inf, -1) and (1, inf) and do the derivative twice. If you look at the graphs, you will see that the slope is always positive, which is why the absolute value is needed. The version without the absolute value only works if x>1.

@aguy165 2 жыл бұрын

Can you please post calc 3 vids I am planning to learn it on my own

@HomieSeal 11 ай бұрын

I’ve been trying to figure this out for months now, but I have a question: is this related to e^kx at all? In terms of the repeat and then the best friend. Is there some way to find *all* functions that follow the pattern $f’(x) = f(x)*g(x)$?

@pratiksaha2935 2 жыл бұрын

In the inverse secant part, with the sec^2x - 1 = tan^2x. If you put the root over from tan^2 it's easy to get 1/ root(x^2 - 1) but i didn't get why another x is being multiplied (if you simply go following the identity). Am an 11th grader.

@rody3199 2 жыл бұрын

You could think of their syllables for derivatives of tanx and cotx. 2 syllables: tan-gent ==> se-cant 3 syllables: co-tan-gent ==> co-se-cant

@pranavkondapalli9306 2 жыл бұрын

you can also think in terms of geometry. In a circle, there are two types of lines. Tangents and Secants. So its kinda obvious how those two functions would be linked

@FreshBeatles 2 жыл бұрын

or just remember that theyre both secant.....just one is co-secant lol

@aleksandarcvetkovski1784 3 ай бұрын

Now make a video with derivatives of hyperbolic trig functions

@m.isworld2562 2 жыл бұрын

how many channels do you even have

@dominicellis1867 11 ай бұрын

Why are there no parabolic trig functions?

@bprpcalculusbasics 11 ай бұрын

I have them on another video.

@dominicellis1867 11 ай бұрын

@@bprpcalculusbasics is there any application of such a function? Would solar panels with parabaloid surfaces use parabolic trig functions?

@syedinayat3548 2 жыл бұрын

great when will you upload limits video

@jojo-nr3yb 2 жыл бұрын

Co functions are “complicated” meaning they get a “-“

@fanamatakecick97 2 жыл бұрын

Wait, if x = sin(θ) and d/dx arcsin(x) = 1/sqrt(1 - x^2), then wouldn’t that make d/dx arcsin(x) = sec(θ)?

@gamerdio2503 2 жыл бұрын

Yes, but we want our answer in terms of x

@fanamatakecick97 2 жыл бұрын

@@gamerdio2503 It was just something i noticed

@kevinpari9500 3 ай бұрын

ez money

@ghijklabcdef 2 жыл бұрын

@haleyanderson2258 2 жыл бұрын

why is he holding a pokeball? lol

@carultch 2 жыл бұрын

It's his microphone.

@tusharjawane9056 2 жыл бұрын

Third hell yeah Hey did you really read my comment what's up with that black t shirt Don't tell me you are really turning heel

@xinpingdonohoe3978 2 жыл бұрын

I don't understand.

@bprpcalculusbasics 2 жыл бұрын

???

@pneujai 2 жыл бұрын

i have another ways but only people who speak cantonese can understand

@bprpcalculusbasics 2 жыл бұрын

I can understand the basic conversational Cantonese. I wonder what it is. 😆

@pneujai 2 жыл бұрын

@@bprpcalculusbasics it's not perfect (or maybe even far-fetched for some) but a famous maths teacher (Herman Yeung) teaches it it's "十個錫錫" and 錫 means 吻, it has similar pronunciation to sec 十個, so it's tan (yea not ten) tan sec sec to differentiate tan: sec sec (look from left to right) to differentiate sec: sec tan (look from right to left) by this and 凡是微分c字頭就變負數, it's easy to work out csc, and cot

@bprpcalculusbasics 2 жыл бұрын

@@pneujai ahhh I got that part 😆