Question

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___

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

partial derivative with respect...

Answer 5

Yep, because z is your function.

Answer 6

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

Answer 7

Okay!

Answer 8

Just a min.

Answer 9

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

Answer 10

So now when you input (1,1) for (x,y), what do you get as your value for \(\dfrac{\partial x}{\partial z}\)?

Answer 11

it think it should be

Answer 12

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

Answer 13

@surjithayer you are right

Answer 14

Yes that is what i got @credmond

Answer 15

you do the next one

Answer 16

Sooo...

Is it just

2/ 2 (3x+2y)^1/2 ?

Answer 17

which gives you 2/2 sqrt (5)

Answer 18

There you go \(\checkmark\)

Answer 19

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