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Implicit Differntation

  • Thread starter Iron_Brute
  • Start date
  • #1
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I've been working on this problem for a while and can't see my mistake, in the book the answer is stated as being 3, but I end up getting 13.5.

Homework Statement


If x^2+3y^2+2y = 10; dx/dt = 2, x=3 and y = -1 find dy/dt

The Attempt at a Solution


d/dt[x^2+3y^2+2y] = d/dt[10]

3x^2 (dx/dt) + 6y(dy/dt) + 2 (dy/dt) = 0

6y (dy/dt) + 2 (dy/dt) = -3x^2 (dx/dt)

dy/dt (6y+2) = -3x^2 (dx/dt)

dy/dt = -3x^2 (dx/dt) / 6x+2

dy /dt = -3(3^2)(2) / 6(3)+2 = 13.5
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi Iron_Brute! :smile:

(try using the X2 tag just above the Reply box :wink:)
If x^2+3y^2+2y = 10; dx/dt = 2, x=3 and y = -1 find dy/dt

3x^2 (dx/dt) + 6y(dy/dt) + 2 (dy/dt) = 0
erm :redface:

either it's x3 in the question or it's 2x in the derivative :wink:
 
  • #3
19
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Hi Iron_Brute! :smile:

(try using the X2 tag just above the Reply box :wink:)


erm :redface:

either it's x3 in the question or it's 2x in the derivative :wink:
Ugh I can't believe it, it's x^2 in the text but I wrote x^3 on my sheet. Thanks for the help (and the tip on writing the exponents didn't know that), I can't believe I spent so much time looking my problem over and didn't see that. :blushing:
 

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