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lili.gallegos

  • one year ago

Use implicit differentiation to find an equation of the tangent line to the curve. x^5y^5=32, tangent at (2,1)

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  1. freckles
    • one year ago
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    know product rule, power rule, constant rule, and chain rule?

  2. freckles
    • one year ago
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    or if you want to make this really easy take the 5th root of both sides

  3. rvc
    • one year ago
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    if you know all the three rules mentioned by freckles then you can easily solve it :)

  4. rvc
    • one year ago
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    if you take the fifth root the equation would be : xy=2

  5. rvc
    • one year ago
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    slope : \(\Large \frac{dy}{dx}\)

  6. lili.gallegos
    • one year ago
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    Can one of you walk me through this ? Step by step ?

  7. rvc
    • one year ago
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    equation of tangent : \[\rm y-y_{1}=\frac{ dy }{ dx }(x-x_{1})\]

  8. lili.gallegos
    • one year ago
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    What about the derivative ?

  9. freckles
    • one year ago
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    you need to apply the rules (or at least some) to differentiate xy=2

  10. freckles
    • one year ago
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    xy is a product so you would use the product rule to differentiate xy

  11. freckles
    • one year ago
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    2 is a constant the constant rule says derivative of a constant is 0

  12. freckles
    • one year ago
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    (xy)'=0 can you apply the product rule to find (xy)'

  13. rvc
    • one year ago
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    you can go through this : Basic Derivatives http://openstudy.com/study#/updates/5550950fe4b061b8579d7c1d

  14. lili.gallegos
    • one year ago
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    What about the derivative ?

  15. freckles
    • one year ago
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    to differentiate is to find the derivative

  16. freckles
    • one year ago
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    (xy)' means find the derivative of the product of x and y

  17. freckles
    • one year ago
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    do you know how to find the derivative of the product of x and y

  18. freckles
    • one year ago
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    do you know the product rule?

  19. freckles
    • one year ago
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    actually if you don't know the product rule @rvc has posted for you in that link

  20. lili.gallegos
    • one year ago
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    Yes I know the product rule ..

  21. freckles
    • one year ago
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    so apply the product rule to find (xy)'

  22. rvc
    • one year ago
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    yep :) you may have a look at that

  23. rvc
    • one year ago
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    good then go for it apply the product rule

  24. lili.gallegos
    • one year ago
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    Okay thank you !

  25. rvc
    • one year ago
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    All the best

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