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Calculus problem- Implicit differentiation

  1. Mar 22, 2013 #1
    1. The problem statement, all variables and given/known data
    e^y = x(y-1) answer must be in implicit form


    2. Relevant equations



    3. The attempt at a solution
    I literally have no idea how to do this problem. I have the answer, but thats it.
    The answer is dy/dx(e^y) = x(dy/dx) + y - 1
     
  2. jcsd
  3. Mar 22, 2013 #2

    jedishrfu

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    I think you differentiate both sides and on the left side use the product rule.
     
  4. Mar 22, 2013 #3

    Fredrik

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    I think that would be "your other left". :wink:

    Chain rule on the left, product rule on the right.
     
  5. Mar 22, 2013 #4

    jedishrfu

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    Yeah sorry I'm somewhat dislexic. My mother would paint a red dot on my right shoe so I'd get it right.
     
  6. Mar 22, 2013 #5

    SammyS

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    I suppose you've out grown those shoes by now.
     
  7. Mar 22, 2013 #6

    jedishrfu

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    Yeah, I wear Tevas now.
     
  8. Mar 22, 2013 #7
    I think the best way to do this is to remember that everything is a function of x. It's just a slightly obscure application of product and chain rule.
     
    Last edited: Mar 23, 2013
  9. Mar 22, 2013 #8

    Fredrik

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    You're giving away too much information X89. That first equality was the only thing we left for the OP to figure out on his own.
     
  10. Mar 22, 2013 #9
    how bout now?
     
  11. Mar 23, 2013 #10

    Fredrik

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    That's better. However, you are using the symbol ##\phi## inconsistently. Your notations suggest that it's first a function from ℝ into ℝ, and then a function from ℝ2 into ℝ. And if ##\phi:\mathbb R^2\to\mathbb R##, then the last equality isn't true in general. It's true when ##\phi## is defined by ##\phi(y(x),z)=e^{y(x)}## for all ##x,z\in\mathbb R##, because this ##\phi## is actually independent of the second variable, but in general
    $$\frac{d}{dx}\phi(y(x),x) =\frac{\partial\phi}{\partial y}\frac{dy}{dx} +\frac{\partial\phi}{\partial x}.$$
     
  12. Mar 23, 2013 #11
    Ah, yeah I see what you mean. When I was deleting stuff from my original post I didn't do a very careful job at all. I'm pretty sure it originally made sense. I might as well just delete my post.
    Edit: Actually on that note, is it possible to delete posts or just edit them?
     
  13. Mar 23, 2013 #12

    Fredrik

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    Give me a second. I'll see if I can delete this one.

    Nope. When I click edit and go into advanced mode, I don't see a delete option. I think the admins have disabled the edit feature in the homework forums to prevent people from deleting the evidence that they got help from someone.

    When you delete a post from another forum, the moderators can still see it, so if you have written something really embarassing, edit out the contents first, save the changes, and then delete. :smile:
     
  14. Mar 23, 2013 #13

    SammyS

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    For one thing, in my experience, it's not possible to delete a post after you can no longer "Edit" it. I think that's after something like 700 minutes.

    More importantly, according to the rules of this Forum, you are not allowed to delete the Original Post of a thread -- especially after someone has responded to it. Doing such will result in a warning or infraction from the Moderators.
     
  15. Mar 23, 2013 #14

    HallsofIvy

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    You're lucky. My mother would just stomp on my left foot. (Or was that my drill sergeant? I keep getting them confused.)
     
  16. Mar 23, 2013 #15

    jedishrfu

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    How'd you know my Mom was a drill sgt? Hey just kidding Mom. Mom? Gotta go... Hup Two three four...
     
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