Question

s(x,y)= sqrt(u(x,y)^2 + v(x,y)^2. Use the chain rule to find ∂s/∂x and ∂s/∂y. Problem : u(x,y) = x(1-x)(1-2y) and V(x,y) = y(y-1)(1-2x);

Answer 1

where you getting into trouble with this?

Answer 2

like how do you use the given information to solve the problem

Answer 3

i like to start by reading it, then I apply it ...

Answer 4

\[s(x,y)= (u(x,y)^2 + v(x,y)^2)^{1/2}\]
this is the problem right?

Answer 5

i have no clue what to do

Answer 6

while calculating del(s)/del(y) (NOT same as ds/dy, 'del' means partial differentiation) you just differentiate with respect to y keeping all other stuff (including any other variable like x constant). ditto for del(s)/(del(x)

Answer 7

no thats the given information

Answer 8

thats's the dimensions given

Answer 9

\[sx= (u(x,y)^2 + v(x,y)^2)'^{1/2}*(u(x,y)^2 + v(x,y)^2)'\]

\[(u(x,y)^2 + v(x,y)^2)'=u(x,y)'^2 + v(x,y)'^2\]

\[u(x,y)'^2=2(u(x,y))*ux\]

\[v(x,y)'^2=2(v(x,y))*vx\]

Answer 10

thats the basic setup for tackling this problem; the rest is just in making it specific

Answer 11

Problem : u(x,y) = x(1-x)(1-2y) and V(x,y) = y(y-1)(1-2x); what is this then?

Answer 12

\[s_x=\frac{2u(x,y)u_x + 2v(x,y)v_x}{2(u(x,y)^2 + v(x,y)^2)^{1/2}}\]

\[s_x=\frac{u(x,y)u_x + v(x,y)v_x}{(u(x,y)^2 + v(x,y)^2)^{1/2}}\]

Answer 13

expand out u and v and take the partials like normal

Answer 14

or play with them as is and product rul them into submission

Answer 15

thats's tough lol

Answer 16

it only tough if you let everyone else do it for you ;)

give it a shot so I can see where youre having troubles

Answer 17

\[u_x = x'(1-x)(1-2y)+x(1-x)'(1-2y)+x(1-x)(1-2y)'\]

\[u_x = (1-x)(1-2y)+x(-1)(1-2y)+x(1-x)(0)\]

not to bad

Answer 18

wait what did you do here ^

Answer 19

its a little thing that we learned back in calc1 called the product rule ....

Answer 20

ohhh

Answer 21

\[D[fgh]=f'gh+fg'h+fgh'\]

Answer 22

\[u_y = x'(1-x)(1-2y)+x(1-x)'(1-2y)+x(1-x)(1-2y)'\]

\[u_y = 0(1-x)(1-2y)+x(0)(1-2y)+x(1-x)(-2)\]

thats the playground for Uy

Answer 23

so I dont think this issue is so much of not knowing WHAT to do, but rather there is just alot of clutter to figure out WHEN to do it ....

Answer 24

yea but i still don't get how its gonna solve the problem

Answer 25

like i am confused

Answer 26

after youve determined where the pices go, and how they are derived; you just fit them all together

Answer 27

put ux where ux goes, vx where vx goes; u where u goes, v where v goes; and call it a day :)

Answer 28

\[\large s_x=\frac{u(x,y)u_x + v(x,y)v_x}{(u(x,y)^2 + v(x,y)^2)^{1/2}}\]

Answer 29

ohhh ok i get it

Answer 30

thank you

Answer 31

yep, good luck ;)

Answer 32

wait i have one more insane problem. this problem is scary

Answer 33

to clean that one up id prolly shorthand it to:
\[\large s_x=\frac{u(u_x) + v(v_x)}{\sqrt{u^2 + v^2}}\]
and sy is the same basic set up

\[\large s_y=\frac{u(u_y) + v(v_y)}{\sqrt{u^2 + v^2}}\]

Answer 34

okay

Answer 35

type up your insane problem to the left and see who bites ;)

Answer 36

i typed it lol

Answer 37

can you give the answer for this one

Answer 38

http://openstudy.com/code-of-conduct

"Don't devalue the question/answer process!"
>Don't provide someone with just the answer - explain the process,
and help guide them through understanding the problem.

If there is someplace that you are still struggling with in the problem, please feel free to be specific as to what it is that is not quite clicking.

Answer 39

lol i think i got it