credmond
  • credmond
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___
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Jhannybean
  • Jhannybean
\[z = \sqrt{3x+2y}\]\[\frac{\partial x}{\partial z} = ~?\]\[\frac{\partial y}{\partial z} = ~?\]
Jhannybean
  • Jhannybean
ell me what those two are first. Then we'll continue :D
credmond
  • credmond
So x with respect to z and y with respect to z, right?

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credmond
  • credmond
partial derivative with respect...
Jhannybean
  • Jhannybean
Yep, because z is your function.
Jhannybean
  • Jhannybean
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
credmond
  • credmond
Okay!
Jhannybean
  • Jhannybean
Just a min.
Jhannybean
  • Jhannybean
\[\frac{\partial x}{\partial z} = \frac{1}{2}(3x+2y)^{-1/2}(3) = \frac{3}{2(3x+2y)^{1/2}}\]
Jhannybean
  • Jhannybean
So now when you input (1,1) for (x,y), what do you get as your value for \(\dfrac{\partial x}{\partial z}\)?
anonymous
  • anonymous
it think it should be |dw:1441433075557:dw|
credmond
  • credmond
Oh okay! So you get 3/2 sqrt 5?
Jhannybean
  • Jhannybean
@surjithayer you are right
Jhannybean
  • Jhannybean
Yes that is what i got @credmond
Jhannybean
  • Jhannybean
you do the next one
credmond
  • credmond
Sooo... Is it just 2/ 2 (3x+2y)^1/2 ?
credmond
  • credmond
which gives you 2/2 sqrt (5)
Jhannybean
  • Jhannybean
There you go \(\checkmark\)
credmond
  • credmond
Aaaaaah! Thank you sooooo much I really appreciate the help! You are the best! :)
Jhannybean
  • Jhannybean
No problem :D

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