## 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___

1. Jhannybean

$z = \sqrt{3x+2y}$$\frac{\partial x}{\partial z} = ~?$$\frac{\partial y}{\partial z} = ~?$

2. Jhannybean

ell me what those two are first. Then we'll continue :D

3. credmond

So x with respect to z and y with respect to z, right?

4. credmond

partial derivative with respect...

5. Jhannybean

Yep, because z is your function.

6. 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

7. credmond

Okay!

8. Jhannybean

Just a min.

9. Jhannybean

$\frac{\partial x}{\partial z} = \frac{1}{2}(3x+2y)^{-1/2}(3) = \frac{3}{2(3x+2y)^{1/2}}$

10. Jhannybean

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

it think it should be |dw:1441433075557:dw|

12. credmond

Oh okay! So you get 3/2 sqrt 5?

13. Jhannybean

@surjithayer you are right

14. Jhannybean

Yes that is what i got @credmond

15. Jhannybean

you do the next one

16. credmond

Sooo... Is it just 2/ 2 (3x+2y)^1/2 ?

17. credmond

which gives you 2/2 sqrt (5)

18. Jhannybean

There you go $$\checkmark$$

19. credmond

Aaaaaah! Thank you sooooo much I really appreciate the help! You are the best! :)

20. Jhannybean

No problem :D