Implicit Differentiation | Differentiation when you only have an equation, not an explicit function

[@taia-b8f]

For the other people that got stuck looking at dy/dx = -2x/2y(x). Basically, just keep solving the equation that he shows you and keep treating dy/dx as a variable. 2x + 2y(x)dy/dx = 0 2y(x)dy/dx = -2x dy/dx = -2x/2y(x) dy/dx = -x/y(x) dy/dx = -x/y

[@NINJA-tf6bf]

Thank you very much ❤ Your explanation is mind blowing 🤯

[@andybrice2711]

Thinking of y as the function y(x) was very helpful here. I've never quite understood before why this can be treated as an application of the chain rule.

[@mohammadfallahzade2110]

You are a great Teacher thank you so much

[@mnada72]

Great 👍, very informative, thanks.

[@gustavopalma9451]

Nice explanation.

[@gordongoodwin6279]

I love your videos but it would be great if you could re-do this one when you have time. As others have noted, it wasn't very clear how you arrived at the 2y(x) dy/dx as the derivative of the composite function. I understand it now but it wasn't clear in the video

[@SandeepKumar-qu9dh]

Happy teacher's day sir

[@studentsofmathematics8995]

dear which software are you used for presenting lecture? please guid me. thanks

[@florentinosanchez3969]

Very nice video

[@captainphysix]

great video!

[@FRC_CR]

I have to say up until this point the course was great but you seemingly assumed that from 4:03 adding some dydx randomly made sense. I have no clue how you got to that conclusion and you didn't really explain it. Can you help me please?

[@gordongoodwin6279]

Agree this part was poorly explained compared to everything else. The dy/dx is the derivative of the inside function (y), which flows from the chain rule. In other words, y(x)^2 is a composite function. The outside is the squaring act, so derivative of outside with respect to inside is 2y(x). Then we multiply it by the derivative of the inside. Well, the inside is just (y), so the derivative is dy/dx. Putting it all together we get 2y(x) multiplied by dy/dx

[@Celtics-x4w]

@@gordongoodwin6279h

[@eyesack3606]

Old Sheldon.

[@qualquan]

bad

[@twisted4872]

That was a horrible explanation . . .you murdered it.

[@nebilzeleke3703]

are u edmonds cc student ????

[@NINJA-tf6bf]

You truly are twisted