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Chain Rule

  1. Oct 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Differentiate gif.gif

    2. Relevant equations


    3. The attempt at a solution
    gif.gif gif.gif gif.gif
    du/dx = cos(x) dv/du=cos(u) dg/dv=cos(v)

    dg/dx = dg/dv.dv/du.du/dx
    = cosx.cos(sinx).cos(sin(sinx))

    I know the answer is correct but my issue is in the understanding of the solution given. I understand it all except the u = sin(x). The approach I take is to work from the inside to the outside by finding u as the inner most and g(v) as the outermost. What I don't understand is why isn't u = x? isnt that the inner most?

    Thanks.
     
  2. jcsd
  3. Oct 5, 2015 #2

    Mark44

    Staff: Mentor

    You should never make the substitution u = x, because it's not useful. In that case, all you're doing is changing the name of the variable from x to u. The innermost function of x is sin(x).
     
  4. Oct 5, 2015 #3
    Ah. So I should think of it as the innermost FUNCTION of x not just x. So its all about the functions? What if it was x^2 instead of the x? would the innermost function be x^2?
     
  5. Oct 5, 2015 #4

    Mark44

    Staff: Mentor

    Yes, because this is a function of x, rather than just plain x.
     
  6. Oct 5, 2015 #5
    Perfect. Thanks so much!
     
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