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A run of the mill Implicit Differentiation

  • #1

Homework Statement



Use Implicit Differentiation to find y' of the equation 5x^2+ 3xy+y^2=15


2. The attempt at a solution

y'= (-10x-5y)/3x

I would like to know if I did this right. Im not very confident in my math sometimes that why I came here. If i did this wrong will you please steer me right. Also if anyone could tell me how to put an equation in more like how you would write it I would appreciate that very much. (As in not the linear fashion I have done)
 

Answers and Replies

  • #2
3,003
2
I don't think this is correct. But, I have not done this in awhile. I think your problem is in the 2nd term [itex]3xy[/itex]. You have a product rule here.

You have [itex]\frac{d}{dx}[3xy]=3*\frac{d}{dx}[xy][/itex]. Now what is [itex] \frac{d}{dx}[xy][/itex] ? I.e, what is the product rule?
 
  • #3
when i did the product rule i got 3y+3xy'
 
  • #4
zcd
200
0
Group the terms with y' and separate the terms without y' into the other side of the equation. Then you can factor out y' from one side.
 
  • #5
I did that last time then the 3y and the and the 2y (previously y^2) combine to 5y then negative after I subtract it over. what answer did you get? Also I believe I may have posted this in the wrong thread, its just a problem on a study guide.

So after doing what you said I again got the same answer.
 
  • #6
zcd
200
0
You can't combine 3y and 2y because 2y is in the form (2y*y') by chain rule. 3y is a term without y', so the equation is actually 10x + 3y = -3x*y' -2y*y' (and then factor from there).
 
  • #7
oh damn it your right lol thanks thats where i thought i may have gone wrong
 

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