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anonymous
 one year ago
d/dx m(x) where m(x) is the tangent line to curve x^2+xyy^2=1 at point (2,3)
anonymous
 one year ago
d/dx m(x) where m(x) is the tangent line to curve x^2+xyy^2=1 at point (2,3)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my work: \( 2x+y+xy'2yy'=0\\ 2x+y=2yy'xy'\\ 2x+y=y'(2yx)\\ \dfrac{dy}{dx}=\dfrac{2x+y}{2yx} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i just plug the point in now? or do I use yy1=m(xx1) somehow

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Since m'(x)=the slope m at (2,3), y'(2) should equal m'(x).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure I understand what the question is asking? is 7 the answer?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1\(\dfrac{d}{dx}(m(x))\) means : after you got m(x), take derivative of it again.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1and then plug (2,3) in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's been like 2 years since I took a calc class, was helping someone with this question. thank you both

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444436902647:dw The question is asking for the slope of the tangent line m(x), which should be the same as the slope of the curve at (2,3), by definition of the tangent. that is why m'(x)=slope of tangent line = y'(2,3)
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