Calculus - Derivatives - Implicit Differentiation (1 of 3)

This video is part of an eight 9 part lecture series that continues and builds upon the previous 8 part derivative lectures.

[djtfan]

Amazing. I've been losing my mind over why whenever you derive x (or an independent variable) you "don't" chain rule, but whenever something else finds its way into the equation, such as a dependent y variable, we have to chain rule. One 4 min video clears everything up. Cheers professor!

[yousefashry]

my full respect mr michael you are the best tutor in the world for me, greetings from egypt

[EP-rqpn]

Wow, I couldn't wrap my mind around why we used dy/dx for these but you make it so clear. That makes so much sense, thank you very much Professor!

[kingmaker]

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[jan-willemreens]

...Als ik uw presentatie goed begrepen heb, dan kun je met behulp van Impliciet differentiëren zowel functies als relaties (in dit geval een cirkel als relatie), in z'n totaliteit differentiëren. In dat geval krijg je dus een formule voor de afgeleide y' uitgedrukt in zowel x als y. Anders moet je de cirkelvergelijking eerst expliciet oplossen voor y, en dat betekent dat je formules krijgt van twee halve cirkels, die natuurlijk ieder afzonderlijk genomen wel functies zijn, en dus volgens de bekende expliciete manier gedifferentiëerd kunnen worden (2 keer differentiëren dus). Maar dat kost natuurlijk veel meer tijd om uit te voeren. Wat mij is opgevallen, is dat je bij differentiëren niet de Kettingregel moet vergeten, vooral bij termen met y daarin, anders mis je dy/dx waar het uiteindelijk allemaal om draait; dat is juist hetgeen wat je wil vinden! (dy/dx= .... ). Een opvallend handige algemene manier van differentiëren, Professor Michel... Merci, Jan-W

[junjun]

I was struggling to understand this part(I was able to use it as tool, but I didn't know why) but now I understand so clearly! thank you

[MuthuLakshmi-kicw]

We can also do this by
y=(50-x^2)^0.5

[TomAustinIII]

X is either 5 or negative 5 and y is the same but of opposite magnitude

[WolfPup-gbze]

Really good videos. I've watched many of your videos. As for the derivative of y squared, I like to think of it as first taking the derivative of y squared to y then multiplying it by the derivative of y to x.

[meelba-tube]

good explanations you are a TOP MATHS LECTURERE for me . I Am from ETHIOPIA.

[xxpnvxx]

Thank you very much for your time and dedication Sir. Your videos have helped me a lot.

[puertoricosanto]

a very fine explanation that cleared a doubt, thanks

[johanpeter]

Thank you for all the videos, you are doing good work.

[thejohn]

So using this, it doesn't matter what is on the right hand side of the equation as long as it is a natural number? E.g. it can be 100, 50, 10, 000, 25, but the answer will always be the same.

[maddywilliams]

Why do maths youtube accounts allow advertisements on their videos which are aimed at putting them out of business.