Question

What is implicit differentiation?

Answer 1

@lgbasallote

Answer 2

@Chlorophyll
@sauravshakya
@Hero

Answer 3

@mukushla

Answer 4

Sorry for tagging y'all, but I really need help.

Answer 5

http://www.hostsrv.com/webmaa/app1/MSP/webm1010/implicit

Answer 6

What do u want to know?

Answer 7

I still am not getting it. Can you explain me what it is?

Answer 8

Have u tried KHANACADEMY videos

Answer 9

um so if we implicit to y, we may not know what y(t) is. so we use chain rule and say y*(dy/dt)

Answer 10

its great

Answer 11

When y can't be expressed in terms of x "only". then y is implicit function of x

Answer 12

its all about taking derivative without knowing explicitly what y depends on.

Answer 13

for y = x
y*(dy/dt) = 1
(dy/dt) = 1/y

Answer 14

@cwrw238 do you have an idea?

Answer 15

I swear im not lying.

Answer 16

what you do is differentiate the function:
ex:
y=x^2+1
dy/dx = 2x And it's done, but:

y^2=x^2
d(y^2)/dx = 2x
dy/dx * 2y = 2x
so
dy/dx = x/y

Answer 17

Suppose \[ x^2 + 3 y^2 =1\]
then
2 x + 6y y' =0
6yy'=-2 x
y'=x/(3y)

Answer 18

To be honest, I still don't get it. :(

Answer 19

you have to find the y' also called f'(x) or also dy/dx, so derivate by x and move thing to get your solution

Answer 20

Read this
http://tutorial.math.lamar.edu/Classes/CalcI/ImplicitDIff.aspx

Answer 21

an example is
differentiate x^2 y + y^2 = 4 with respect to x
you treat y as a function of x
so y *2x + x^2*dy/dx + 2y * dy/dx = 0

using product rule and chain rule

Answer 22

@eliassaab Yes, sir. The fact that I couldn't get the concept at Paul's Notes brought me here to ask this question.

Answer 23

you then find dy/dx in terms of x and y

Answer 24

when we explicite, we are saying y = f(x) so y is dependent on x
so when we explicite differentiate we are doing so with respect to the x that we know y depends on.

now with implicite, we do not know that for y = x that y depends on x. so we make no assumtions when we differentiate.

thus y = x
y*(dy/dt) = 1 (lhs = chain rule)

Answer 25

sorry dy/dx

Answer 26

exactly, you only need to derive, what do you haven't understand, try to make an exercise, it helps!

Answer 27

example of implicit function is
circle formula

x^2 + y^2 = 9

which implies that y is a function of x

Answer 28

try resolve that! :D

Answer 29

Really sorry, guys. Haven't gotten it yet :(

Answer 30

See the step
1) differentiate:
2x+2y*y' = 0
2) move
y'=-x/y
3)have a party

Answer 31

here you can see that it is really a circle! : http://www.wolframalpha.com/input/?i=y'=-x/y

Answer 32

D':

Answer 33

Step by step, slowly:
y^2+x^3+x=1
what is the derivative?

Answer 34

\[{dy^2 \over dx} + 3x^2 + 1 = 0\]

Answer 35

I don't know if that is it... I'm just a beginner!

Answer 36

Ok, I'm sorry, you're right, now derive the y

Answer 37

dy^2/dx = ?

Answer 38

I don't know...

Answer 39

dy^2/dx = 2y*dy/dx using the chain rule, right?

Answer 40

I don't understand! :'(
Yes, I do know the chain rule... but I don't know the application of it here!!! ='(

Answer 41

Where's the outside and inside function?

Answer 42

y is a function the derivative of y is the derivative like is a variable multiply the derivative of y, this is the chain rule right?
(f(g(x)))'=f'(g(x))*g'(x)*x' you understand?

Answer 43

y is the outside function, the inside function is the part with the x, but at you doesn't interest, just writr y', you don't need to calculate it

Answer 44

@descripter37: Wait a second, I'm working on it on another site... I'd return back to you in a minute :)

Answer 45

Ok, tell me if you get it :D

Answer 46

Let f(x) = x^2
f^2(x) = x^4 ..
Then, d/dx (f^2(x)) = 4x^3 ( As we know the basic rule ).
from f(x), d/dx (f^2(x)) = d/dx (x^2)^2 = d/dx (f(x)^2) = 2 (f(x)) d/dx f(x) .. lol i hope you understand.. just clarified what was @decripter37 saying

Answer 47

Ok, so when we don't know what \(y \) is in respect to \(x\), we leave it like that and call it an unknown function of \(x\).

Answer 48

I'm working on it... no need to waste your time more :P

Answer 49

Thank you alL!

Answer 50

Yuhuuuu sorry for all the time, but I'm not very well on English, I'm italian :3 good derivatives

Answer 51

No worries. Ciao!

Answer 52

and remember http://fc05.deviantart.net/fs70/i/2011/088/f/6/don__t_drink_and_derive_by_fire_camel-d3cr4vs.png

Answer 53

Have you been to Venice?

Answer 54

looool

Answer 55

No, I'm close to Rome :)

Answer 56

Is Milan close to Rome?

Answer 57

Streets of italy ♥

Answer 58

Considering that 580 kilometres is close :p

Answer 59

Ehr, no it's very distant, I'm on the center of Italy but if 580 km is close... maybe yes!! XD

Answer 60

Sigh, in all the world people think about Italy only north and south, mode, and pizza, us at the center are ignored! XD