Derivative of Inverse Functions Examples & Practice Problems - Calculus

This calculus video tutorial explains how to find the derivative of an inverse function. It contains plenty of examples and practice problems for you to master the concept. it shows you how to find the inverse function f^-1(x) from f(x) and how to calculate [f^-1(x)]' in terms of x and y. It also shows you how to calculate the slope of the tangent line using the derivative. In addition, it shows you how to calculate the derivative of the inverse function using implicit differentiation - dy/dx. Examples include polynomial and square root / radical functions.
Derivatives - Limit Definition: • Definition of the Deri...
Derivatives - Alternate Limit Definition: • Alternate Form of The ...
Derivatives - The Constant Rule: • The Constant Rule For ...
Derivatives - The Power Rule: • The Power Rule For Der...
Derivatives - Constant Multiple Rule: • The Constant Multiple ...
Derivatives - Polynomial Functions: • Derivatives of Polynom...
Derivatives - Sine and Cosine: • Derivative of Sine and...
Derivatives - Trigonometric Functions: • Derivatives of Trigono...
Derivatives - Limits: • Limits and Derivatives
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Derivatives - Tangent Line: • How To Find The Equati...
Derivatives - Horizontal Tangent Line: • How to Find The Point ...
The Equation of The Normal Line: • How To Find The Equati...
The Equation of The Secant Line: • How To Find The Equati...
Average and Instantaneous Velocity: • Average Velocity and I...
Instantaneous Rate of Change: • Instantaneous Rate of ...
Derivatives - Rational Functions: • Derivatives of Rationa...
Derivatives - Radical Functions: • Derivatives of Radical...
Derivatives - Fractions: • How To Find The Deriva...
Derivatives - Higher Order: • Higher Order Derivatives
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Derivatives - Simplifying: • Simplifying Derivatives
Derivatives - Product Rule - f*g: • Product Rule For Deriv...
Derivatives - Product Rule - f*g*h: • Product Rule With 3 Fu...
Derivatives - Product Rule - f*g*h*k: • Product Rule With 4 Fu...
Derivatives - Quotient Rule: • Quotient Rule For Deri...
Derivatives - Chain Rule: • Chain Rule For Finding...
Chain Rule With Trig Functions: • How To Find The Deriva...
Chain Rule - Harder Examples: • Calculus - Chain Rule ...
Chain Rule - Triple SQRT(x): • Find The Derivative Us...
Derivatives - Composite Functions: • Derivatives of Composi...
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Implicit Differentiation: • Implicit Differentiation
Derivatives - Inverse Trig Functions: • Derivatives of Inverse...
Derivatives - Exponential Functions: • Derivatives of Exponen...
Derivatives - Logarithmic Functions: • Derivative of Logarith...
Logarithmic Differentiation: • Introduction to Logari...
Derivatives - Using Logarithms: • Finding Derivatives Us...
Derivatives - Inverse Functions: • Derivatives of Inverse...
Derivatives - Differentiation Rules: • Basic Differentiation ...
Derivatives - Function Notations: • dy/dx, d/dx, and dy/dt...
Derivatives - The Reciprocal Rule: • The Reciprocal Rule an...
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Introduction to Limits: • Calculus 1 - Introduct...
Introduction to Related Rates: • Introduction to Relate...
Calculus 1 Final Exam Review: • Calculus 1 Final Exam ...
Full-Length Exams and Worksheets: bit.ly/4990rzU

[@TheOrganicChemistryTutor]

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me studying for my last cal exam in senior year

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Me

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Taking mine tomorrow 👀

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So..what happened?

[@actuallystuff]

my prof took one whole lecture to explain it and most of the class still didn't get it. This way wayyyyy shorter and was easy to understand too, thanks king

[@AM-md4ps]

I understand this to a certain degree but I’m also lost

[@caroe.3237]

I really wish you would put y' so it's not confusing which is which

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[@hye6158]

this is literally the hardest of the derivatives... im watching this the the third time and i dont get it :(

[@niina.5190]

i feel you T-T

[@KillerBlader2118]

@@nononnomonohjghdgdshrsrhsjgd same this is the most difficult of the derivatives for me so far..

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I am watching ts like an hour before my calc test, this dude made what my teacher has been teaching us for weeks so damn easy to understand holy shit

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ngl my brain hurts

[@sematagzade4692]

This teacher’s explanation literally is better than everyone

[@colins9616]

@ 4:39 when he says you add dy/dx onto the y derivative, that just means it's a coefficient or something you are multiplying with y. So you can divide dy/dx just like any other number. It is only used for a derivative of y. So this means if you are using a formula to find an implicit derivative, you only have to tack on dy/dx to the y's that are derived, for instance if ysquared becomes 2y. If any of the y's stay the same in the derivative, they don't need a dy/dx.

[@Nacerwork]

I thank God everyday for your existence!

[@Rickby]

Yeah this is the first video I’m really lost on, did I skip something prior to inverse functions?

[@hanstamarasteinke3643]

on your third method of finding the inverse derivative when converting from square root to power and using power rule, you said (1/2-1 ) is the same as 1/2-(2/2)=1. wouldn't the correct answer be -1/2?

[@hanstamarasteinke3643]

nevermind, i watched further and see that you corrected your mistake

[@MrYogiknight]

i just looked threw the comments instantly also and I was like am I the only dumb ass and you saved the embarrassment.

[@pkus]

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[@yennako]

this is hella confusing 😭😭

[@_senator-armstrong]

Welcome to calculus

[@bryceodom3386]

I'm pretty sure you're trying to find the tan line of the inverse function at X=2, but you said you found the tangent line of the original function, y=x^2+2x+1 , at x=2. To find the tan line of the original function you take derivative of the original function y=x^2+2x+1 and plug in 2 which gives you mTan=6 so y=6(x-2)+9 is the tangent line at x=2 of the function y=x^2+2x+1.

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[@ammar3354]

I'm sooo lost

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[@hellozukohere6514]

@@moisesinfante8470 I swear nothing is helping me understand this inverse bs

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i love u, u explained it better than my calc 2 teacher

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[@6dance99]

I thought I got it but then i looked at the comments and now im all fucked up again

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[@Nemoguzapomnit]

Thx for your videos! Btw I've noticed that we can just find the slope for original function and then just substitute it in 1/a, where a is a slope of original function.

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[@antoniorubio602]

I dont think you can find the derivative of the inverse function for your second example because the function is not invertible right?

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[@Algebrainiac]

Great vid! Although I do wonder… what if f(x) is a trig function? And you’re asked to find the derivative of the inverse? I’m pretty sure you’d have to do the inverse trig functions and then take the derivative but I’m not sure

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[@dx6295]

3:31 why don't need to consider -sqrt(x+7) when square root both side?

[@aliaskarbekishev8152]

the same question

[@samirmattout282]

At 12:57 when you said that x = ( y+1)^2 then y + 1 = square root of x, why can't y+1 also be - square root of x?

[@aesthete8237]

This video is great However, I got confused about this 17:32. The slope of tangent line is 1/6 using this inverse function method. But when I tried to use limits to find the slope I got 6 which is contradicting to the first answer. I just want to ask; is 1/6 the slope for the inverse function or the original function? If yes, then why it's not the same answer if you use limits to find the slope of the tangent line? Pls... notice and answer me. I'm really confused about it.

[@andrewlong7432]

This is right because 6 is the slope of your f(x) function. We know that this is correct because the slopes of a function and its inverse are reciprocals. This proves that the slope of the inverse is correctly 1/6

[@JuliuSeizure]

@@andrewlong7432when he said the question, he said find the slope of the tangent line of this function, not the inverse function

[@JuliuSeizure]

I had the same issue, i was like differentiate and substitute! Differentiate and substitute!…? What the heck are you doing??? I guess the question is wrong I’m thankful for the reply above me, the slope of a function and that if it’s inverse are reciprocal.. interesting. Sorry for the cringey comment, basically there was a problem with the question. I got 6 too. What’s this you’re saying about limits though? Differentiation from first principle?

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Great video!

[@andreypopov6166]

read chapter from 3 books, watched 2 videos....and still don't understand this dances with inverses :) i dont want to memorise but to understand...Anyway thank you!

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BLESS

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Those 27 min, I watched them in more than hour *_*

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[@ryanmelsness3667]

I'm still confused RIP

[@babs_iq3066]

Did anyone else isolate y for the last problem just for the challenge

[@maemillanes5357]

How are you supposed to do it when it’s just a graph w/ no given function and they want you to sketch the inverse derivative??? 😐

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[@outofpocket72]

Awesome video but I can’t find anything helpful on composite functions. For example, finding f’(3) and f(x) = (g(x)) type problems where g(3) = 4 and g’(3) = 7 and all that.

[@nathanhocking8073]

Well, in your example, if f(x) = g(x) and g'(3) = 7, then f'(3) =7. But in a generalized sense for finding the derivative of the inverse of f(g(x)), then first you solve for the composite function. For instance, let's say f(x) = 2x-3 and g(x) = x²-3. To solve for a composite function, you take the inner function and treat it as the x of the outer function. That would mean that f(g(x)) = 2(x²-3)-3 which simplifies to 2x²-9. We can treat this function as a new function and call it, say, h(x). So h(x) = f(g(x)) = 2x²-9. We then take the inverse of h(x), which would be x = 2h⁻¹(x)²-9. In order to isolate h⁻¹(x), we first add 9 to both sides, then divide both sides by 2, then take the square root of both sides. This leaves us with √((x+9)/2) = h⁻¹(x). We can then plug that equation into the formula taught in the video, and that will give the derivative of the inverse of f(g(x)), which in this case, would be 1/(4(√((x+9)/2))).

[@jacobfalk4827]

You didn't use trig fncns. I'm crying

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The studypug ad never fails to irritate me

[@harirajagopal3979]

3 ways to find inverse function summary starts at 8:20

[@newton6031]

thanks i go it

[@user-kx2yc5kw9e]

why the 4:51 is 2y

[@mamadujalloh9278]

all you have to do is take the derivative of the inverse the same way you would for any other number. No need to use the formula

[@reubenwilliammpembe667]

you are the best!!!

[@wandering-willow6091]

Ok 1:34 if inverse ftn of x is equal to y and y is a ftn of x that means f inverse of x is equal to f of x? how is that even possible??😭

[@aurorachee]

Dude why you know like everything from chem till cal???

[@garrettzaporowski2170]

Professor literally told me we’re not allowed to just switch the x and y how tf do I find the inverse lmao

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[@arifcalskan4933]

you king

[@xSabir-hc7wj]

how is y = x^2 - 7 and x = y^2 - 7, wouldn't sighs change if u re arrange it??

[@bryceodom3386]

you're not rearranging the function. All you're doing is switching X for Y and Y for X.

[@fletcherk2294]

Talk to fast for me to understand

[@Nemoguzapomnit]

How come that x^2-7 has an inverse if it doesn't pass HLT?

[@katharinak.8731]

Because its x^2, meaning, it is a parabola and a negative value in x will always come out positive

[@Nemoguzapomnit]

@@katharinak.8731 2^2-7 is positive?

[@katharinak.8731]

@@Nemoguzapomnit No, what I am saying is that (-2)^2 is the same as (2)^2

[@Nemoguzapomnit]

@@katharinak.8731 yeah that's true. But my question was about horizontal line test

[@katharinak.8731]

@@Nemoguzapomnit right, of you draw out x^2 - 7 it is a parabola, and y values cannot occur twice for it to pass a hlt

[@DevSingh-ld7xb]

I love you

[@randallhalejr.4247]

Da derivadive

[@liamhoward2208]

Quadratic equations do not have inverses. They are not one-to-one.

[@jeremaemagno2836]

I'm so so lost

[@user-ug8hp2bd5q]

ابداععععععععععععععع

[@cmilay5808]

14:17

[@arifcalskan4933]

bbut im sooo losst

[@petertran5419]

F(x)=y F-inv(y)=x F-inv(x) =y is WRONG

[@mabihinafff942]

الكلى و الدرقية دمرتها يورو اسس هول بينس موني