Question

Can someonehelp me with this question (calc 3)

Answer 1

Perhaps.

Answer 2

Express partial u/partial x, partial u/partial y, partial u /partial z, as a function of x,y,z both by using the chain rule and by expressing u directly in terms of x,y,z before differentiating

Answer 3

u=(p-q)/(q-r)

Answer 4

p=x+y+z and q=x-y+z

Answer 5

i am jus sort of confused at the moment on how to do this if somen can give me a hint

Answer 6

Okay, so they ask you to do this two different ways. The second way is just by substituting into u first. That is:
u = (p-q)/ (q-r) gives:
u = ((x+y+z)-(x-y+z))/((x-y+z)-r) = (2y)/((x-y+z)-r)

Btw, is there an equation given for r also? Or just p and q?

Answer 7

oh yeah, r=x+y-z

Answer 8

Ah =) Good.

Answer 9

Okay, so substituting for p,q, and r, and then simplifying gives us:
u = (2y) / (2z-2y)
See that?
And then we can just differentiate that with respect to x, y, and z individually.

Answer 10

For example to do du/dx, I look at u = y/(z-y) as if everything but x was a constant. Since there is no x in the equation, the derivative du/dx becomes 0.

Answer 11

but what about using the chain rule, thats what i am having problems with

Answer 12

Okay to do that part I get: du/dx = du/dp*dp/dx + du/dq*dq/dx + du/dr*dr/dx

Answer 13

Right, Amistre?

Answer 14

okay, i got you from there, that's what i was confused on, thanks SmoothMath

Answer 15

yes

Answer 16

Okay, cool. Let me know if you have any trouble taking over from there, NightShade.

Answer 17

I perfer a different notaiton tho

U(q,p,r)

UpPx + UqQx + UrRx

Answer 18

so it this a function of three variables (one independent variable and three intermediate variabeles)?

Answer 19

Where the capital letter is the function and the lowercase letter is the variable being differentiated with respect to? Seems shorter to write, I suppose. Surprised I've never seen it written that way.

Answer 20

\[\binom{U_p}{P_x}+\binom{U_q}{Q_x}+\binom{U_r}{R_x}\]

where the () are just multiplied together

Answer 21

Yes, U(p,q,r); P(x,y,z); etc ...

Answer 22

would this be a du/dt=... or something else

Answer 23

I'm not sure what you're asking. t wasn't one of the variables involved, so du/dt seems irrelevant.