Implicit Differentiation and Linear Approximation | MIT 18.01SC Single Variable Calculus, Fall 2010

[Nickuncle]

1 person got rejected from M.I.T.

[Perulaiz]

someone remind me why do i need this to make/fix cars..

[MrMaxen92]

Now, i'm not a math genuis, but the lectures from MIT (and since i've had an somewhat understanding before for these type of calculations) are really good in my opinion, despite the fact that my ordinary math lessons is in Swedish :D

[lucirz]

amazing thanks

[FatBoySlim696]

You'd think MIT could upload some HD videos. Or at least standard definition.

[darnit006]

6:28 why is it 2? shouldnt it be 1?

[hellomynameis1234567]

@darnit006 he moved over the 1 from the other side to make it 2

[sugarcoatedsour]

Implicit differentiation is just differentiating both sides of an equation using the chain rule and taking the derivative with respect to x (unless otherwise noted). In related rates, you shift that to taking derivatives with respect to individual units.For linear approximation, the key to understanding this is to relate it to algebra. Linear approximation is simply the point-slope formula. Instead of y-y1=m(x-x1) think y-f(x)=f'(x)(Δx). Solving for y gives you y=f(x)+f'(x)(Δx).

[prettysaphire]

Wow. I'm not planning on doing math at uni but it'd be pretty cool if I could understand this when I finish my further maths A level...

[MyMIXmedia]

can anyone explain how this type of mathamatics is used in real life. Can you build cars or computers with this maths.

What use does this have.

x(w) x1, x1=(x/w) x2 1/x(w) +0 x/w 1/0

wtf is shit like i wrote mean.

[sugarcoatedsour]

this wouldnt be used to build a computer per se, but it could be used in the engineering of cars. Linear approximation comes in handy in many engineering and physics applications. For example, linear approximation is used in GPS satellites to offset the time difference (special relativity) in order to ensure that the time is consistent with that time one earth because of the offset of the curvature of earth surface in relation to the curvature of an orbit.

[KeyOfAm]

@MyMIXmedia

All math is useful

[llemes4011]

It took me a couple seconds to realize that linear approximation = 1st degree Taylor Polynomial haha

[brutishquito]

i was lost from 00:01 to 10:17 .

[taalipas]

After minute 8:00 , the frame-rate changed and its really on nerves!

[ghghghkkkkkkkkkkkkkk]

Alright, im confused. How does he get from w(-1)=0 to w(1)=0 ?

[pksonu1991]

not bad,,,,,,,,,,,............

[x1x2x3ct]

n1

[TeslaWasHere]

It's not too bad, but that's an interesting hefty equation to start with. Good video.

[coutxxStatix]

I love how the only part i understand is the simple algebra, but i still find it interesting ^^

[marts1233]

@coutxxStatix what didnt you understand?? he uses tayler series to get the approximation, it's very simple

[hamsterpoop]

The chicken!

[tafeykey]

What is the difference between implicitly differentiating than just normal differentiation? Also, is there such a thing as explicit differentiation? What are the differences?

[MagicBoterham]

@tafeykey Implicit differentiation is differentiation of an implicit function.

Explicit differentiation is differentiation of an explicit function.

An implicit function is a function where the variables are not explicitly defined.

Example y*x=3 is implicit

y=3/x is explicit

Explicit functions are of the form y=f(x), if that sort of relation is not defined the function is implicit.

[jinalkothari]

@tafeykey Implicit functions are those, like he said, which are not directly definable. That is f(x) = something is not available. The normal differentiation is where you use explicit functions.