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anonymous
 5 years ago
Use chain rule to find dy/dx for the given value of x.
y+ (u1/u+1)^1/2
u=sqrt x1; for x=34/9
anonymous
 5 years ago
Use chain rule to find dy/dx for the given value of x. y+ (u1/u+1)^1/2 u=sqrt x1; for x=34/9

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first step I get 1/2 (u1/u+1)^1/2 not sure what to do next. I am brain dead at the moment.

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1what was original function did you replace dx with du du = dx/2sqrt(x1)

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1sorry i think im mistaken, ignore what i just said but you will use du

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1take what you have and you will multiply it by derivative of (u1)/(u+1) use quotient rule

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do I do with the ^1/2. I need to bring that infront of the equation and subtract 1 from the 1/2, is that correct?

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1correct looks like you did that already in the 1st post

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, after that do I use quotient rule?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok after that I get (u+1)(u1)/(u+1)^2 which ends up being 2/(u+1)^2

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1correct, now simplify and then you have to multiply by du ans replace u with x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do I need to take derivative of U first?

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1yes sorry that was what i meant by du (derivative of u) then replace all the u's with sqrt(x1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so derivative of u would be 1/2(x1)^1/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do I replace the u with 1/2(x1)^1/2 and also replace the x with 34/9 or will that be a different step?

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1no remember what you assigned u as u=sqrt(x1) 1/2(x1)^1/2 just gets multiplied on the outside Last step will be replacing x with 34/9

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so 2/(u+1)^2 * 1/2(x1)^1/2 U= sqrt x1 and x=34/9 ????

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1yes but dont forget what you had originally 1/2 (u1/u+1)^1/2 thats part of it still too

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am lost now would it be 1/2 [(sqrt x1)1]/sqrt [(x1)+1]^1/2 * 1/2 (34/91)^1/2 ????

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.12/(u+1)^2 correct just add this part with u = sqrt(x1) 2/[sqrt(x1)+1]^2 also replace all the x's with 34/9 i know this one has a lot of parts

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this answer really seems wrong, I am sure I did something wrong in my math but I get 2025/136

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1hmm i worked it out and got 27/320 ill write it out so you can compare \[\frac{dy}{dx} = \frac{1}{(2\sqrt{(34/9)1})(\sqrt{(34/9)1}+1)^{2}\sqrt{\frac{\sqrt{(34/9)1}1}{\sqrt{(34/9)1}+1}}}\] 34/9 1 =25/9 sqrt of that is 5/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why did you take 1 over everything

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1because everything had a power of 1/2 right, that means its on the denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh I see now, didn't think of that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what equation I am using to replace with?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is hard for me to explain to you what I am talking about without showing you my paper or pointing to what you have written. I can see where the (sqrt 34/9)11/(sqrt 34/9)1+1 came from, the deriviative of original problem 1/2(u1/u+1)^1/2. But not the (2sqrt 34/9)1) (sqrt 34/9 1+1)^2

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1ahh it comes from using the chain rule, we are multiplying derivative of original times derivative of inside function ex: f(x) = sqrt(x^2 +1) its a composite function, i say g(x) = x^2+1 f(g) = sqrt(g) f'(g) = 1/2sqrt(g) g'(x) = 2x whats important is the derivative of original is product of these 2 derivatives f'(x) = g'(x)*f'(g) f'(x) = 2x*1/2sqrt(x^2+1) so at the end we replace x^2 +1 back in for g
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