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anonymous
 5 years ago
Find the slope of the tangent line to the curve 2(x^2+y^2)^2=25(x^2y^2) at the point (3,1).
anonymous
 5 years ago
Find the slope of the tangent line to the curve 2(x^2+y^2)^2=25(x^2y^2) at the point (3,1).

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the slope of the tangent line is given by the dy/dx. So this question is on implicit differentiation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea i'm only having problems differentiatiog the right side of the equation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.02(x^2+y^2)^2=25(x^2y^2) Differentiate both sides with respect to x: 4(x^2 + y^2)[2x + 2y(dy/dx)] = 25[2x  2y(dy/dx)]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know how to continue from there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but for the right side isn't it 25 (2xy^2 y' +x^22y)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The slope of the tangent line is given by the dy/dx, and now the question is to determine the slope at (3,1). So substitute x= 3 and y = 1 into the equation and then rearrange it to get the dy/dx. Would you like to try it first?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Why is it 25 (2xy^2 y' +x^22y)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0multiplying 25 by the derivative of x^2y^2+x^2 the derivative of y^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the right side is only 25(x^2  y^2). Differentiate it you have (d/dx)[25(x^2  y^2)] = 25 (d/dx)[x^2  y^2] = 25 [(d/dx)(x^2)  (d/dx)(y^2)] = 25 [2x  2y (dy/dx)]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, i still don't understand how did you get yours...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So are you able to continue it now? :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, we have x=3 and y=1, so substituting in we get 4(x^2 + y^2)[2x + 2y(dy/dx)] = 25[2x  2y(dy/dx)] 4(9 + 1)[(6) + 2(dy/dx)] = 25[(6)  2(dy/dx)] 240 + 80(dy/dx) = 150  50(dy/dx) 130 (dy/dx) = 90 dy/dx = 9/13

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i thought i had to simplify until i find y' then i substitute in... oh well it makes sense though, thanks :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can also rearrange to find your y' then only you substitute. But I think in this case, it is easier to substitute to get your y'
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