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Implicit diferentiation

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Find dy/dx of this equation -
    [tex] y*sec(x)=3x*tan(y) [/tex]


    2. Relevant equations

    -product rule
    -derivative of sec(x) with respect to x is sec(x)tan(x) i believe
    -derivative of tan(x) is sec^2(x) i believe


    3. The attempt at a solution

    [tex] y*sec(x)=3x*tan(y) [/tex]

    [tex] y*sec(x)*tan(x)+sec(x) \frac{dy}{dx}=3x*sec^2(y)\frac{dy}{dx}+3*tan(y)[/tex]

    [tex] sec(x)\frac{dy}{dx}-3x*sec^2(x)\frac{dy}{dx}=3*tan(y) -y*sec(x)*tan(x)[/tex]

    [tex]\frac{dy}{dx}(sec(x)-3x*sec^2(x))= 3*tan(y) -y*sec(x)*tan(x)[/tex]

    [tex]\frac{dy}{dx}= \frac{3*tan(y) -y*sec(x)*tan(x)}{sec(x)-3x*sec^2(y)} [/tex]

    That last line is my solution. I do homework online and every time i enter this it says it is wrong. So where am I going wrong?
     
  2. jcsd
  3. Oct 17, 2009 #2
    Your last line is correct. Perhaps the problem is with how you entered it. What is the exact string that you entered?
     
  4. Oct 17, 2009 #3
    I entered it the almost the exact same way except for sec^2 . I typed it in as (sec(y))^2. Are you sure I am right?
     
  5. Oct 17, 2009 #4
    That's the unambiguous way to write it. I have checked the differentiation independently. In your derivation, you switched one of the y's for an x, but you got the last line, so I assume that was a typo. If your parentheses are all correct in your typed version, I would go ahead and show the professor the problem and your solution personally.
     
  6. Oct 17, 2009 #5
    Ok. Thanks for double checking for me then.
     
  7. Oct 19, 2009 #6
    FIGURED IT OUT. The answer I have here is correct. Its a hundred percent correct. dy/dx does equal that value that i posted in my original post. TOO BAD THEY ASKED FOR dx/dy. Its the classic case of not reading the question correctly :P. I'm so used to taking the derivative of dy/dx I just made the assumption that it was dy/dx. Once I found out that it was dx/dy I was able to get the answer right on the first try :D. Sorry about causing you any trouble if I did.

    Many thanks for your checking
    -hover
     
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