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How to find a general expression for derivative

  1. Oct 4, 2012 #1
    Hello everybody,

    I am trying to solve this problem but I can't find an answer reading my book :(

    Let z=F(u,w,x) where u=f(x,y) and w=g(x,y)

    (i) find a general expression for Dxz
    (ii) verify your answer in the case where F(u,w,x)=w3-2ux, f(x,y)=4xy-x+1 and g(x,y)=y+xy2

    Many thanks
     
  2. jcsd
  3. Oct 4, 2012 #2

    Ray Vickson

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    Other than trying to find it in your book, what else have you tried? Forum rules require you to show your work.

    RGV
     
  4. Oct 4, 2012 #3
    Yes, I've read the rules, sorry. the point is that I don't know where to stard with :( more than the just the solution I would like some references to books or links where I can study the problem..

    thx again
     
  5. Oct 4, 2012 #4

    Ray Vickson

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    So, are you saying you have never encountered such material before? You have never heard of the chain rule?

    RGV
     
  6. Oct 4, 2012 #5
    sadly no :( I have to take a test of basic math knowledge and we only have some notes to prepare... but ty for the hint of the chain rule :)
     
  7. Oct 4, 2012 #6
    ok, thx to RVG who explained me where to look for the solution I think I have solved it:

    (i): Dz/Dx=DF/Du*DU/Dx+DF/Dw*DW/Dx+DF/Dx

    (ii) Dz/Dx= -2x(4y-1)+3w2y2-2u

    Is it right? it is fairly easy once discovered wich formula to use (if I've used the right one of course)
     
  8. Oct 4, 2012 #7

    Ray Vickson

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    Yes, you have made a correct start in part (i) and you have a correct result in part (ii) (although I guess there is an issue of whether or not to plug in the actual values of u and w and do a complete simplification).

    RGV
     
  9. Oct 4, 2012 #8

    SammyS

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    Yes, that looks good.

    I used WolframAlpha to compare:
    Your answer after substituting for w & u.

    First substituting for w & u in F(u, w, x) then getting the partial derivative of that expression with respect to x . ​
     
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