how I remember all the trig and inverse trig derivatives
ฝัง
- เผยแพร่เมื่อ 1 ส.ค. 2024
- 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
-----------------------------
Are you loving the math content on my channel and want to see more of it? I'm thrilled to hear that! You can show your support and help me create even better content by becoming a patron on Patreon 👉 / blackpenredpen or snagging a stylish math shirt or hoodie from my creator store 👉 amzn.to/3qBeuw6. Every bit of support means the world to me and motivates me to keep bringing you the best math lessons out there! So join me on this journey and let's tackle math together!
-----------------------------
#calculus #math #bprpcalculus
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.
Yea same here. And the students say they don’t like the triangle until they see all the identities.
@@bprpcalculusbasicsWhy don't you call them arcsin, arccos, arctan, arccot, arcsec, arccsc? It's more easy, not?
@@user-ex1hp8ph3pnot really , when you use the cos^-1(x) it’s easier cus u just need to add the negative exponent
You will definitely be useful to me next year. In 11th grade. :D
Believe me...not just useful he will be a tool
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.
what an absolute legend, i was just struggling to remember these derivatives and saw this video. huge thanks for saving my grades!
Glad to help. Best wishes to you 😃
You are great!!
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!
Thanks so much! really appreciated it
so helpful thank you!!
WOW!! Great lesson! 😊
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?
I c baj
thank you
Great video!!!!! It's so helpful for a cal 1 student like me😎😎
I LOVE YOU
You are great!!
thanks bro bprp
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!!
Me forgetting basic arithmetic as a calc student
This helps alot💜
That is awesome act
great video! the most useful to me was tan and sec are best friends same with cot csc
Good COntent really helped me fr
Thank you !!!!
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]). ◼
Gr8 video man
Thank you sir
Lovely.
A real hero
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.
How I remember all the trig and inverse trig derivatives?
just calculus: Video 7:15 long.
FAST!: "Don't forget them"
😂
Now make a video with derivatives of hyperbolic trig functions
this video is underrated
cool!
I used to have ways to remember, but now with so much practice they are literally set in my brain like stone
Can you please post calc 3 vids I am planning to learn it on my own
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.
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 $f’(x) = f(x)*g(x)$?
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.
Oh yea it depends on the domain where they define the sec^-1. See 5:01
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.
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
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
or just remember that theyre both secant.....just one is co-secant lol
how many channels do you even have
Why are there no parabolic trig functions?
I have them on another video.
@@bprpcalculusbasics is there any application of such a function? Would solar panels with parabaloid surfaces use parabolic trig functions?
great when will you upload limits video
Co functions are “complicated” meaning they get a “-“
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)?
Yes, but we want our answer in terms of x
@@gamerdio2503
It was just something i noticed
ez money
Hi
why is he holding a pokeball? lol
It's his microphone.
i have another ways but only people who speak cantonese can understand
I can understand the basic conversational Cantonese. I wonder what it is. 😆
@@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
@@pneujai ahhh I got that part 😆
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
I don't understand.
???