Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

Some relationships cannot be represented by an explicit function. For example, x_+y_=1. Implicit differentiation helps us find _dy/dx even for relationships like that. This is done using the chain _rule, and viewing y as an implicit function of x. For example, according to the chain rule, the derivative of y_ would be 2y_(dy/dx). Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[malihareza]

"Let me do that in a different color..."-sal in every lessom

[beastlybob]

Okay, i just learned in 8 minutes what my calculus professor failed to teach in 2 hours of class time!

[mariakhan]

There have been a thousand maths teachers on YouTube, but nothing compares to Sal ♥️ thanks, sir

[JBMgo]

Leibniz's notation is so much easier for the Chain Rule and its applications! Try to learn implicit diferenciation using the f-prime notation and you will have a hard time.

[brendonbalascan]

I didn't learn this right in calc 1 and i'm revisiting it for my calc 3 class and it's completely blowing my mind how this works. You can really just treat the derivatives as operators? that's insane.

[xobk]

Just when I start feeling like calculus is becoming an endless series of garbled numbers and symbols, it goes and wows me again with something like this!

[dAvrilthebear]

Thank you, Khan! As usual, simple, clear and concise.

[ajstordeur]

I love this man its 2am I'm up to doing delta math having not a single clue what implicit differentiation is and this man just saved my life for my test tomorrow. I saw that green chack on my delta math and screamed yes so loud that I'm baffled my parents didn't wake up. I love this man.

[EmpyreanLightASMR]

3:30 I think this is what i've been hunting for across the universe. In fact, I didn't even know d/dx MEANT anything other than "you're deriving with respect to x"... but you're making it sound like it's vastly more important.

[sundayjohnson]

Sal is the best math teacher online that I've watched so far

[gameprofile]

You guys are doing wonderful job . Keep it up . Love Khan academy .

[katrinaWHATx]

whoa, perfect timing! I have an exam on this tomorrow. thank you so much! I finally get it.

[rampant]

This was so helpful, especially putting d/dx (y(x))^2 thank you very much. Made my life much easier

[manuelkarner]

4:29 "might be a little bit cleare" lol I searched 2 intense hours for exactly this chaining explanation (without knowing)
THANKS !

[pandapanda]

Was stuck on a problem for 2 hours now, until i found this amazing explanation
As always Khan Academy to the rescue!

[gilbertobarajas]

Thank you, Sal and company! This helps so much

[isabelamcneilly-anta]

omg i needed help on hw on explicit differentiation and this is the EXACT problem

[EDUARDO]

This was a great example, and finally, implicit diff clicked for me.

[Dij]

You make it all so simple, thank you!!! When I saw this in lecture, was scared lol

[enkephalin]

This contributes little to solving other differential equation, but at least it's not nothing. Breaking the terms down into separate differential operators does help clarify a novel variant of the problem, but that's not often enough.