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Implicit differentiation help

  • Thread starter cj2222
  • Start date
  • #1
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can someone show me step by step how to find dy/dx of y=1/(x+y) using implicit differentiation?
 

Answers and Replies

  • #2
hunt_mat
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if [tex]y=1/[x+y)[/tex] then [tex]y^{2}+xy=1[/tex]. Differentiate to obtain:
[tex]
2y\frac{dy}{dx}+y+x\frac{dy}{dx}=0
[/tex]
Re-arrange to obtain dy/dx
 
  • #3
hunt_mat
Homework Helper
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Or failing that [tex]y^{2}+xy-1=0[/tex] in a quadratic in y, solve this equation and you should have y=y(x) which is easy to differentiate!
 
  • #4
182
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hunt_mat is correct. Rearranging is much quicker, but taking the quadratic route is very useful to check your answer.

Edit: If I let v = x + y, then y = 1/v and dy/dx = -1/v^2 dv/dx. However, continuing this does not give me the right answer; why not? EDIT: Nevermind, I figured it out. :)
 
Last edited:

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