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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___
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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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[z = \sqrt{3x+2y}\]\[\frac{\partial x}{\partial z} = ~?\]\[\frac{\partial y}{\partial z} = ~?\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2ell me what those two are first. Then we'll continue :D

credmond
 one year ago
Best ResponseYou've already chosen the best response.0So x with respect to z and y with respect to z, right?

credmond
 one year ago
Best ResponseYou've already chosen the best response.0partial derivative with respect...

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Yep, because z is your function.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2if 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{\partial x}{\partial z} = \frac{1}{2}(3x+2y)^{1/2}(3) = \frac{3}{2(3x+2y)^{1/2}}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2So now when you input (1,1) for (x,y), what do you get as your value for \(\dfrac{\partial x}{\partial z}\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it think it should be dw:1441433075557:dw

credmond
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay! So you get 3/2 sqrt 5?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2@surjithayer you are right

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Yes that is what i got @credmond

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2you do the next one

credmond
 one year ago
Best ResponseYou've already chosen the best response.0Sooo... Is it just 2/ 2 (3x+2y)^1/2 ?

credmond
 one year ago
Best ResponseYou've already chosen the best response.0which gives you 2/2 sqrt (5)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2There you go \(\checkmark\)

credmond
 one year ago
Best ResponseYou've already chosen the best response.0Aaaaaah! Thank you sooooo much I really appreciate the help! You are the best! :)
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