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math help plz (solve by implicit differentiation)
    #11248196 -

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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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11248219 -

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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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11248245 -

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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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11248249 -

Whats this wrt business

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Re: math help plz (solve by implicit differentiation) [Re: Chespirito]
    #11248252 -

with respect to


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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11248257 -

:discorex:

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249005 -

Formula: 0

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


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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249111 -

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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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249124 -

dy/dx of xy is just y.

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249128 -

Use the product rule and the chain rule.

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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Re: math help plz (solve by implicit differentiation) [Re: memes]
    #11249132 -

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


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


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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249137 -

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

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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249142 -

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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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249158 -

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

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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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249165 -

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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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249172 -

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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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249191 -

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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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249212 -

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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Re: math help plz (solve by implicit differentiation) [Re: learningtofly]
    #11249229 -

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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Re: math help plz (solve by implicit differentiation) [Re: DieCommie]
    #11249266 -

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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