Explaining the Implicit Differentiation : Equation of tangent line to a curve in an implicit form

In this session on Implicit differentiation of a relation, you will learn about the followings
The Concept of implicit differentiation | Why do we need implicit differentiation | Implicit and Explicit forms | Chain Rule for implicit differentation | Examples of implicit differentiation | Slope of tangent line to curve defined by implicit form | Equation of tangent line to curve defined by implicit form | Tangent line to equation of heart | General Power Rule of Differentiation |
We have seen already the followings :
When and How to use Chain Rule |
Chain Rule for Trigonometric functions | Chain Rule for Polynomial functions | Chain Rule for Rational functions | Chain Rule for Square Root functions | Chain Rule for nth root functions | Chain Rule, Product Rule and Quotient Rule |
#implicit_differentiation #implicitdifferentiation #implicitderivative #implicitfunction #implicitform
#implicitcurve #tangentline #slopeofaline #slopeofatangentline #tangenttocurve #functionsandrelations #functionsandlimits #functionsanddifferentiation
#chainrule #chainruleforderivative #calculus
#differentiation #derivativeformulas #derivatives #derivativesofthefunction #derivative #differential_calculus #differentiation #differentiationoffunction #rateofchange #rateofchangeofquantities #productrule #quotientrule #leibniz #leibniztheorem #leibnrule
#calculus #functions #continuousfunction #discontinuousFunctions
#limitoffunction #mathematics #computerscience #mathforCS
#sukkuriba #sukkuribauniversity

[@abdulsaeedpitafi9773]

I wanted to take a moment to express my appreciation for your enlightening lecture on implicit definition. Your ability to elucidate complex mathematical concepts with such clarity is truly commendable.
The way you seamlessly connected theory with practical examples made the topic come alive for me. It not only enhanced my understanding but also sparked a genuine interest to delve deeper into this subject. Your passion for teaching is evident in every explanation you provide, and it's truly inspiring.
Thank you for your dedication to your students' learning and for sharing your expertise through these videos. I'm looking forward to more insightful lectures that continue to enrich our understanding.

[@CalculusCraze1]

😍💚

[@FoodieMe180]

Well explained sir ❤ Allah pak bless you ,

[@CalculusCraze1]

Thanks

[@NehalSoomro-rt4oc]

Helpful for new students in calculus...

[@geetakhatri5307]

Amazing sir ..keep it up sir ❤❤ today was my paper i did in one hour bcz of your videos sir paper was tough acc to others pr bcz of you videos when i saw paper i said in my heart are mujh to aa raha hai sb... wrna do ghanty lag jaaty😢😢 so thankyou so much sir ..aisi videos banaty rahe..❤

[@CalculusCraze1]

Mehlbaaani😄 thanks 🙂🙂🙂😍

[@saqibnazeer1569]

Mashallah Sir
Well explained ❤

[@CalculusCraze1]

Thanks a lot dear ❤️

[@faxs4_u]

Jeo saein jeo

[@CalculusCraze1]

Thanks a lot for that 🙂

[@Struggler_Apu]

Watching this 30 mins before exam🙂but thank you so much ❤

[@CalculusCraze1]

😳

[@shakoorgilal4231]

❤❤❤

[@CalculusCraze1]

🥰🥰

[@mushtaqueali8722]

ماشاءاللہ سر بہترین 🎉

[@CalculusCraze1]

Thanks

[@Fahadhussainprog]

sir fatah's two favourite words
"Interesting and famous"😂😂

[@CalculusCraze1]

Hahaha... Thanks 😂

[@enjoyinglife5435]

Amazing sir you way of teaching maths 🤩

[@CalculusCraze1]

JazakAllah

[@love_lyrics-5380]

Zabardust Sain🎉🎉❤

[@love_lyrics-5380]

Abdul Sattar is here sain 😊❤

[@hassnainshah3237]

Well explained sir. Thank You 🙏🏻❤

[@CalculusCraze1]

Thanks a lot

[@ammaramirani]

Great Work!

[@CalculusCraze1]

JazakAllah

[@mufeedrind4415]

Good explanation sir ...

[@CalculusCraze1]

JazakAllah

[@mirsarfraz7143]

An excellent effort to deliver on one of the trickiest topics of calculus. Here I want to keep my observations which I found the lecture lacked in it. There is no such thing you mentioned in your lecture, such as the General Power Rule. Yes, the Power Rule does exist, which helps us to differentiate y=x^n. Meanwhile, to differentiate y=(f(x))^n...(i) we use the Chain Rule. To do this, we assume u=f(x)...(ii). Now, by substituting u in equation (i), we have y=u^n(iii). Now we can apply the Chain Rule on equation (ii) and equation (iii) to obtain dy/dx, which you called the General Power Rule.
My point is that to teach the concept of implicit differentiation without actually using the concept of chain rule is injustice with topic and to rely solely on the direct formula you called General power rule would create confusion for the students.You should use proper method which I mentioned above to teach tstudents the concept of implicit differentiation.

[@CalculusCraze1]

Thank you so much for your kind suggestions. Actually my audience is not from department of Mathematics. In other words, this course is taught informally so I have ommitted technicalities. Hopefully I will come up with a rigorous course inshAllah where we will keep all the details and abstraction that is required.

[@CalculusCraze1]

Secondly, the terminology of General Power rule has been used by Ron Larson his calculus book on page 132.

[@KnowledgeCornor]

Good work Sir 🖤

[@CalculusCraze1]

Thanks thanks

[@Muhammad_Ramzan22]

Sir, is there any use of implicit differentiation in real life?

[@CalculusCraze1]

Wherever there is a real world phenomenon described by some implicit function. You can find many especially in dynamical systems, their differentiation is carried out using implicit differentiation.
So many curves are defined using implicit forms so their slopes of tangents are found using implicit differentiation like equation of ⭕.

[@dharanjarshi17]

Sain samjh t sajo achi wayo pr heart g derivation kadahn n wisrandi 😂

[@CalculusCraze1]

Wisran b na khapy 😂😂😂