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Implicit differentiation - Help

  • Thread starter pat666
  • Start date
  • #1
709
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Homework Statement



find y' given x3+y2+x+y=2

Homework Equations





The Attempt at a Solution


dy/dx=3x2+2y(y')+1+y'
I know thats wrong because my 89 gives it as y'=(-3x2+1)/(2y+1), I don't know how to get there though and what happened to the =2.
Thanks
 

Answers and Replies

  • #2
95
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The Attempt at a Solution


dy/dx=3x2+2y(y')+1+y'
I know thats wrong because my 89 gives it as y'=(-3x2+1)/(2y+1), I don't know how to get there though and what happened to the =2.
Thanks
You turned the 2 in the original equation to dy/dx, instead of d(2)/dx, but the rest is correct. You should have 3x2+2y(y')+1+y'=0, then put the non-y terms on the right and factor out y' from 2y(y')+y' and you'll have the book's answer.

It also seems like the correct answer should have (-3x2-1) rather than (-3x2+1).
 
  • #3
709
0
I've gotten closer to the solution but now I'm stuck at
3x^2+1=1-1-y'-2y(y')
3x^2+1=-y'-2y(y')????????

Thanks
 
  • #4
95
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Now factor y' out of -y'-2y(y'). You'll have (-1-2y)y'. Then divide both sides by -1-2y.
 
  • #5
95
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Another thing..
in your last reply, you have =1-1-y'-2y(y'). Where did the 1-1 come from? If this is d(2)/dx, then it's sort of incorrect. The derivative of a constant is always 0; 1-1 is of course equal to zero, but writing 1-1 is sort of confusing for the person who's error checking.
 
  • #6
709
0
yeah, I see what you mean - ill avoid doing that... Thanks for your help.
 

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