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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^2-y^2) at the point (-3,1).

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  1. anonymous
    • 5 years ago
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    the slope of the tangent line is given by the dy/dx. So this question is on implicit differentiation

  2. anonymous
    • 5 years ago
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    yea i'm only having problems differentiatiog the right side of the equation

  3. anonymous
    • 5 years ago
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    differentiating*

  4. anonymous
    • 5 years ago
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    2(x^2+y^2)^2=25(x^2-y^2) Differentiate both sides with respect to x: 4(x^2 + y^2)[2x + 2y(dy/dx)] = 25[2x - 2y(dy/dx)]

  5. anonymous
    • 5 years ago
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    Do you know how to continue from there?

  6. anonymous
    • 5 years ago
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    uhmm not quite

  7. anonymous
    • 5 years ago
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    but for the right side isn't it 25 (2x-y^2 y' +x^2-2y)

  8. anonymous
    • 5 years ago
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    The 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?

  9. anonymous
    • 5 years ago
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    Why is it 25 (2x-y^2 y' +x^2-2y)?

  10. anonymous
    • 5 years ago
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    multiplying 25 by the derivative of x^2-y^2+x^2- the derivative of y^2

  11. anonymous
    • 5 years ago
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    the 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)]

  12. anonymous
    • 5 years ago
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    Sorry, i still don't understand how did you get yours...

  13. anonymous
    • 5 years ago
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    you're right

  14. anonymous
    • 5 years ago
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    So are you able to continue it now? :)

  15. anonymous
    • 5 years ago
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    still stuck :(

  16. anonymous
    • 5 years ago
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    ok, 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

  17. anonymous
    • 5 years ago
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    oh i thought i had to simplify until i find y' then i substitute in... oh well it makes sense though, thanks :)

  18. anonymous
    • 5 years ago
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    you 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'

  19. anonymous
    • 5 years ago
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    you're welcome

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