Question

s(x,y) = x^3 lny + 4y^2e^x find the indicated function Syy (x, y)

Answer 1

I think it's [-X^3/y^(2)] +[8e^(x)]

Answer 2

Yes. it is, but how ? could you show me?

Answer 3

yeah
but give me like 10 15 minutes i'm going to grab something to eat

Answer 4

ok, well you understand that when taking a Sy x is held constant.

Answer 5

yes

Answer 6

okay cool
then what's the derivative of lny?

Answer 7

1/y

Answer 8

?

Answer 9

x^3 is constant and that would stay on the top correct?
next, What is the derivative of 4y^2

Answer 10

yes

Answer 11

8y

Answer 12

e^x is constant
so, what is Sy?

Answer 13

8e^x

Answer 14

not exactly, the answers that we found previously will be Sy. What I mean by that it Sy :x^3/y +8ye^x. These are the answers you gave me. Do you see how it equals that? If not, we can approach it differently.

Answer 15

So Ssubyy = -x^3/y^2 + 8e^x?

Answer 16

remember "x" is constant
so if you want plug in 7 for x just so you get use to the idea

Answer 17

sorry yea that's the answer

Answer 18

Yes.. why are you plugging in 7? I understand Sy = x^3/y + 8ye^x.. I think my question was to find Syy (x,y) =?

Answer 19

oh then you just do a second partial it's the same idea as doing a second derivative and the "7" thing is just case if haven't grasped the idea that the other variable is held constant.

Answer 20

Ic

Answer 21

Are you in Calc 3 or DE?

Answer 22

No.. just very basic business calc

Answer 23

cant imagine doing the regular calc :(

Answer 24

you have to do partials?

Answer 25

Yes.. now to find the local extreme for max and min in 3D

Answer 26

I have another one.. I just can't do figure out should I post it separate?

Answer 27

sure

Answer 28

I just fan you.. thanks for your help

Answer 29

I tried to post it.. but it got stuck
f(x,y) = x/y = y/x find fxx, fxy, and fyy