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Offlinelearningtofly
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math help plz (solve by implicit differentiation)
    #11248196 - 10/14/09 07:05 PM (14 years, 5 months ago)

Solve using implicit differentiation (for y in terms of x)

x - y3 = 0

I don't quite get how this works.

Do i say:

dy x = dy y3
dx        dx

then i dont know?

I got

    1        but that was using the chain rule
3 x^(-2/3)

Edited by learningtofly (10/14/09 07:07 PM)

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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11248219 - 10/14/09 07:08 PM (14 years, 5 months ago)

Take the derivative of each piece separately - remember that 'y' is a function of 'x', so you have to use the chain rule.

Derivative of x w.r.t. x is 1.  Derivative of y^3 w.r.t. x is 3 y^2 dy/dx.  I put that dy/dx in there because of the chain rule.  Then solve for dy/dx.

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11248245 - 10/14/09 07:13 PM (14 years, 5 months ago)

if you say x wrt x = 1 then the x disappears and you get 1 = 3y^2dx/dy ?

or dy/dx = 3y^2


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Edited by learningtofly (10/14/09 07:14 PM)

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InvisibleChespirito
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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11248249 - 10/14/09 07:14 PM (14 years, 5 months ago)

Whats this wrt business

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: Chespirito]
    #11248252 - 10/14/09 07:14 PM (14 years, 5 months ago)

with respect to


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InvisibleChespirito
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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11248257 - 10/14/09 07:14 PM (14 years, 5 months ago)

:discorex:

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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249005 - 10/14/09 08:57 PM (14 years, 5 months ago)

Formula: 0

Formula: 1
Formula: 2
Formula: 3
Formula: 4


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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249111 - 10/14/09 09:15 PM (14 years, 5 months ago)

thanks!

one more question

how would I do

dy of xy
dx

cuz the problem is x2 + xy + y2 = 4 and once again i need to do implicit differentiation.


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Invisiblememes
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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249124 - 10/14/09 09:16 PM (14 years, 5 months ago)

dy/dx of xy is just y.

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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249128 - 10/14/09 09:17 PM (14 years, 5 months ago)

Use the product rule and the chain rule.

Quote:

meams said:
dy/dx of xy is just y.




I assume he means d/dx of xy.  So you get Formula: 0

Edited by DieCommie (10/14/09 09:24 PM)

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: memes]
    #11249132 - 10/14/09 09:18 PM (14 years, 5 months ago)

Quote:

meams said:
dy/dx of xy is just y.




thats what I figured but I kept getting the wrong answer.


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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249137 - 10/14/09 09:19 PM (14 years, 5 months ago)

I guess there isnt really a chain rule in that one.  Check my edit.

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Invisiblememes
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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249142 - 10/14/09 09:19 PM (14 years, 5 months ago)

It's all good.  Be sure to SOLIDIFY this shit in your brain now, it sucks to forget it and need it later.  I just started my masters courses and they're 98% mathematical, 2% theoretical.  I fucking forgot ALL of that shit.  I've been pretty behind these past few weeks but I feel like I'm just about caught up now.

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249158 - 10/14/09 09:22 PM (14 years, 5 months ago)

Quote:

DieCommie said:
Use the product rule and the chain rule.

Quote:

meams said:
dy/dx of xy is just y.




I assume he means d/dx of xy.  So you get Formula: 0




quoted from the book says "Find dy/dx in terms of x and y by implicit differentiation"

x2 + xy + y2 = 4


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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249165 - 10/14/09 09:23 PM (14 years, 5 months ago)

Yes, find dy/dx.  To do that you operate on every term with the derivative operator d/dx, then solve for dy/dx.

dy/dx of xy doesn't really make sense, because dy/dx is a derivative not an operator.

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249172 - 10/14/09 09:24 PM (14 years, 5 months ago)

i'm lost.

so dy/dx just means y'(x) right?

and then i would find d/dy and then d/dx ?


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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249191 - 10/14/09 09:28 PM (14 years, 5 months ago)

bah, Ill LaTeX it out

Formula: 0

Now implicitly take the derivative by applying the Formula: 1operator to each side.

Formula: 2
Formula: 3
Formula: 4
Formula: 5
Then solve for dy/dx.

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249212 - 10/14/09 09:33 PM (14 years, 5 months ago)

in the last line, (dx/dx)(y)+x(dy/dx) why is one dx/dx and the other dy/dx

i understand that d/dx(xy) = d/dx(x+y) = d/dx(x)+d/dx(y) = dx/dx + dy/dx = 1 + dy/dx ... i think?

but why do you have (dx/dx)(y) + x(dy/dx)


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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249229 - 10/14/09 09:38 PM (14 years, 5 months ago)

Quote:

i understand that d/dx(xy) = d/dx(x+y)




That is not true.

I used the product rule to get Formula: 0.  What you are doing to that term is taking the derivative of a product.  So its the derivative of the first times the second plus the derivative of the second times the first.  http://en.wikipedia.org/wiki/Product_rule

So I took the derivative of the first term and got dx/dx and multiplied it by the second term y.  Then I added that to the derivative of the second term, dy/dx and multiplied that by the first term x.  The product rule.

What you and meams wanted to do is not correct because y is a function of x, its y(x).  It is not a constant so the constant multiplier rule you were trying to use is no good.  That is one of the keys to implicit differentiation that students often miss (which is why I stated it first in my first post :smile: ).  y in these problems is a function of x and is not a constant.

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Offlinelearningtofly
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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249266 - 10/14/09 09:44 PM (14 years, 5 months ago)

f'(x)g(x)+g'(x)f(x) yah i know the product rule i just didn't realize you were supposed to use it there.

oh i see so xy really is x multiplied by y(x) aka f(x)g(x) ?

ahhhhhhhh math  :justdontknow:

EDIT: so it's like f(x) = x, g(x) = y

then dx/dx(y)+(x)(dy/dx) right?



EDIT again: :facepalm: one of the reasons I was so confused was that I read the answer to the wrong problem.

Do you guys have any tips for being 'dyslexic' with numbers? I often misread problems like this...

ex. 1. xy + z = A
      2. gh + b = L

I will read 1. as xy + b = A a lot. if you understand what im saying

Edited by learningtofly (10/14/09 09:51 PM)

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InvisibleDieCommie

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249275 - 10/14/09 09:46 PM (14 years, 5 months ago)

Yep, you got it.  y is a function of x, so it must be treated differently then a normal constant.  In this case it needs the product rule, often times students forget to apply the chain rule as well.  Good luck!

What are you taking this for anyway?  Is this calc 1 or brief calc?

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