Derivatives of Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions - 3 Examples
In this video, we go through three examples to find the derivatives of inverse trigonometric functions. We explore how to differentiate expressions involving inverse sine, inverse cosine, and inverse tangent functions. These examples provide a straightforward approach to understanding the rules and steps required for differentiating inverse trigonometric functions in calculus.
Whether you're a student reviewing for an exam or someone brushing up on calculus skills, this video will make finding derivatives involving inverse trig functions more approachable!

#derivatives #calculus #inversefunctions #trigonometry #math #PatrickJMT #differentiation #calculusproblems #inversetrig #derivativesoftrig #chainrule #productrule #mathhelp #mathtutorial #mathvideos

2/2

You said:
please redo that description and make sure it is formatted for youtube so i can just copy and paste
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Derivatives of Inverse Trigonometric Functions - 3 Examples

In this video, we work through three examples of finding derivatives of inverse trigonometric functions. We explore how to differentiate expressions involving inverse sine, inverse cosine, and inverse tangent functions. You'll learn step-by-step techniques to handle derivatives for functions like
(
sin
⁡
−
1
(
𝑥
)
)
2
(sin
−1
(x))
2
,
cos
⁡
−
1
(
2
𝑡
−
1
)
cos
−1
(
2t−1
​
), and
tan
⁡
−
1
(
𝑥
𝑎
)
+
ln
⁡
𝑥
−
𝑎
𝑥
+
𝑎
tan
−1
(
a
x
​
)+ln
x+a
x−a
​

​
.

By the end of this lesson, you'll have a better grasp of applying derivative rules to inverse trigonometric functions, making these types of calculus problems much more manageable.

#derivatives #calculus #inversefunctions #trigonometry #math #PatrickJMT #differentiation #calculusproblems #inversetrig #derivativesoftrig #chainrule #productrule #mathhelp #mathtutorial #mathvideos

Can you explain reference angles?

[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)

[tzghw]

Thank you very much! I'm taking AP Calculus and my teacher never finishes explaining any of the topics we've learned and she is always telling us to read the book and figure it out by ourselves. Thanks to your videos I am doing so much better in that class.

[catherinekirby]

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

[hajessie]

THANK YOU! In less than 3 minutes you were able to enlighten me on the stuff my professor failed to do in over an hour! You're my savior!

[brianh]

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

[iprocrastinateviayou]

it is so comforting to know ive your help for calc2

[iamshebang]

The past few days I was so lost and clueless during lecture and pretend I understand the professor. I thought I'll flunk this subject. But after watching your videos, oohhh, I suddenly feel like a genius and I'm now eager to attend my class.

[arnelmaghirang]

In 2:27, he's right. whenever you have a square root of variable then you raised it to what number of your index will be cancelled out. square root of variable raised to the exponent which is the same as with the index is cancelled. in your next problem, 1/2 *2=2/2=1.

[avivthebest]

I have a Cal 1 test this friday and I felt like I was gonna fail...then I found this video and now I have some hope!! thanks

[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

[ANILTHEGAME]

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

[Aerex]

@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.

[zeynepayl]

when i started ap calc this year i thought there was no hope so thank you so so so much for these videos!! I cannot thank you enough!

[mizzcachon]

i learned more+faster by watching your videos than attend lecture! Thanks so much!

[Slayn]

i always get confused when to use product rule and when to use chain rule...

[walkerwiggins]

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.

[katielafa]

You are my hero. Such an AMAZING teacher.

[dirronprease]

I hate that you are left handed, but your videos are invaluable!

Thanks for all the help through these videos.

[thabogenny]

oh thank you PAT, ur work means alot 2 some of us..plz keep on doing the good work cz it cn realy brigthten up our the bestest

[fedelfedel]

Man, your examples are the best. Please keep it up.