1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?

  2. jcsd
  3. Oct 5, 2015 #2


    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


    Staff: Mentor

    Yes, because this is a function of x, rather than just plain x.
  6. Oct 5, 2015 #5
    Perfect. Thanks so much!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted