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anonymous
 5 years ago
If u=f(x,y) where x=(e^s)(cos(t)) and y=(e^s)(sin(t)), show that (du/dx)^2 + (du/dy)^2 = (e^(2s))((du/ds)^2+(du/dt)^2))
anonymous
 5 years ago
If u=f(x,y) where x=(e^s)(cos(t)) and y=(e^s)(sin(t)), show that (du/dx)^2 + (du/dy)^2 = (e^(2s))((du/ds)^2+(du/dt)^2))

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0pretty complicated chain rule problem, i'd really appreciate some help on this one

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you mean (du/dx)^2 is that the second derivative ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, its the square of du/dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, its the square of du/dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Its kinda confusing since usually f(x,y) is something like X^2 + y^3 something like that. Another confusing thing about the problem is that you have the derivative of u in respect to x and (du/dx) and derivative of u in respect to y (du/dy) which doesnt make sense.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i mean you can say u= x+ y then the question would make more sense but in that case you have to find (dx/dt) or (dx/ds) or vice versa with y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you mean have x+y be the function? f(x,y)=x+y?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no usually the problem is set up this way f(x,y)= z if z= w/e ( it has an x and a y) where y= (something that has s and t) and x= ( something that has s and t) but your question does not make sense to me. Are you sure you wrote it right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, i copied it exactly.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what does it mean to find du/dx?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0To find the derivative of the function u in respect to x for example lets say u= x^2 if you want to find du/dx = 2* x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok well thanks anyway for your help

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0YES I AM. you really are a hero! the only thing i dont understand is what du/ds and du/dt are equal to, and how you got that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you say u sub x times c, what is c?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, sorry, I use "c" and "s" for cos(t), sin(t) here.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Where I write "NTS", that means, "need to show".

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but you have no idea how messy mine is after working on it for over an hour now. thank you so much!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0du/ds and du/dt...that comes from a result in calculus (chain rule for functions of many variables).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have u = f(x(s,t), y(s,t)). The parameters that do all the 'controlling' in the function are s and t, so you take the partial derivative with respect to them.
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