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credmond

  • one year ago

Let z = sqrt{3x+2y}. Then: The rate of change in z at (1,1) as we change x but hold y fixed is___ and The rate of change in z at (1,1) as we change y but hold x fixed is___

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  1. Jhannybean
    • one year ago
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    \[z = \sqrt{3x+2y}\]\[\frac{\partial x}{\partial z} = ~?\]\[\frac{\partial y}{\partial z} = ~?\]

  2. Jhannybean
    • one year ago
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    ell me what those two are first. Then we'll continue :D

  3. credmond
    • one year ago
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    So x with respect to z and y with respect to z, right?

  4. credmond
    • one year ago
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    partial derivative with respect...

  5. Jhannybean
    • one year ago
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    Yep, because z is your function.

  6. Jhannybean
    • one year ago
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    if we're changing x, then x is our variable and y is our constant. if we're changing y, then y is our variable and x is our constant

  7. credmond
    • one year ago
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    Okay!

  8. Jhannybean
    • one year ago
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    Just a min.

  9. Jhannybean
    • one year ago
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    \[\frac{\partial x}{\partial z} = \frac{1}{2}(3x+2y)^{-1/2}(3) = \frac{3}{2(3x+2y)^{1/2}}\]

  10. Jhannybean
    • one year ago
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    So now when you input (1,1) for (x,y), what do you get as your value for \(\dfrac{\partial x}{\partial z}\)?

  11. anonymous
    • one year ago
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    it think it should be |dw:1441433075557:dw|

  12. credmond
    • one year ago
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    Oh okay! So you get 3/2 sqrt 5?

  13. Jhannybean
    • one year ago
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    @surjithayer you are right

  14. Jhannybean
    • one year ago
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    Yes that is what i got @credmond

  15. Jhannybean
    • one year ago
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    you do the next one

  16. credmond
    • one year ago
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    Sooo... Is it just 2/ 2 (3x+2y)^1/2 ?

  17. credmond
    • one year ago
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    which gives you 2/2 sqrt (5)

  18. Jhannybean
    • one year ago
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    There you go \(\checkmark\)

  19. credmond
    • one year ago
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    Aaaaaah! Thank you sooooo much I really appreciate the help! You are the best! :)

  20. Jhannybean
    • one year ago
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    No problem :D

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