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Homework Help: Implicit differentiaion using the number e (lon-capa)

  1. Feb 29, 2012 #1
    Implicit differentiaion using the number "e" (lon-capa)

    Hello~ :3 this is my first time posting here, so I hope I didn't do anything wrong. I'm currently in Calculus 1, university level, and I have to enter all my answers using lon-capa (evil evil program). In lon-capa:

    *= multiplication sign
    exp= number e (exponents are instead put in parenthesis, as in my answer below)

    1. The problem statement, all variables and given/known data

    Find dy/dx if the curve is defined by

    10 x^2 e^(7 y) + 8 y^4 e^(5 x) = 19.


    3. The attempt at a solution

    This is my lon-capa attempt:
    (10*x^2*7*exp(7*y)+20*x*exp(7*y)+8*y^4*5*exp(5*x))/(-32*y^3*exp(5*x))

    This is a more reasonable-looking version:
    (10x^2*7e(7y)+20x*e(7y)+8y^4*5e(5x))/(-32y^3*e(5x))

    I used both the product rule and implicit differentiation, but lon-capa keeps telling me my answer is wrong. I'm not sure if it's a mistake with the parenthesis or the answer itself, but I'd be grateful for any help/advice.
     
    Last edited: Feb 29, 2012
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  3. Feb 29, 2012 #2

    SammyS

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    Re: Implicit differentiaion using the number "e" (lon-capa)

    Hello Nana-chan. Welcome to PF !

    Show how you did the problem, not just your final result.

    What do you get when implicitly differentiated the following?
    10 x2 e7y + 8 y4 e5x = 19​

    Did you take the derivative with respect to x or with respect to y?

    Did they really ask for dx/dy ?
     
  4. Feb 29, 2012 #3
    Re: Implicit differentiaion using the number "e" (lon-capa)

    Thanks, here's what I did:

    10 x2 e7y + 8 y4 e5x = 19

    I did the product rule on both sides:

    10x^2*e(7y)*7 + 20x*e(7y) + 8y^4*e(5x)*5 + 32y^3*dy/dx*e(5x)= 0

    Then I moved the value that contained dy/dx to the other side:

    10x^2*e(7y)*7 + 20x*e(7y) + 8y^4*e(5x)*5 = 32y^3*dy/dx*e(5x) = (32y^3*e(5x))(dy/dx)

    Then I divided both sides by (32y^3*e(5x)) in order to get dy/dx and got the answer that you saw above.

    And no, I'm sorry, they didn't ask for dx/dy, they asked for dy/dx, I made a typo in my original post, which I will now proceed to edit.
     
  5. Feb 29, 2012 #4

    SammyS

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    Re: Implicit differentiaion using the number "e" (lon-capa)

    (To write superscripts or subscripts, use the "Go Advanced" option for the message window. Then use the X2 or X2 ikon above the message box.)

    You are missing a dydx . See it in red above .
     
  6. Feb 29, 2012 #5
    Re: Implicit differentiaion using the number "e" (lon-capa)

    Ohhh~ you see I wasn't sure if the derivative of 7y would be 7 alone or what you stated above. I entered it in on lon-capa and my answer is now correct! Thank you very much!
     
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