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differentiation chain rule help

Discussion in 'Mathematics' started by fudgesweets, Jan 23, 2011.

  1. fudgesweets

    fudgesweets New commenter

    Hi,

    I was talking to a friend about the chain rule i.e. dy/dx =dy/du X du/dx. She said that technically it is incorrect to say that this works because the 'du's cancel each other out. I didnt quite understand the explanation. Can anyone else explain to me?

    Also if you have for example dy/dx =1 , you can solve this as a differential equation by seperating the variables so you have integ 1 dy = integ 1 dx, but why can you seperate the variables? How does that make sense, isnt dy/dx itself as a whole the gradient.
     
  2. It is "technically" wrong as they are not fractions

    Because integration is the reverse of differentiation and int dy = y

    Are you happy with differentiation from first principles?
     
  3. fudgesweets

    fudgesweets New commenter

    yes i understand differentiation from first principles. I understand they are not fractions but then why can you cancel them out? or can you not and there is something else going on?
     
  4. DM

    DM New commenter

  5. fudgesweets

    fudgesweets New commenter

    thanks DM i have read that post and i now fully understand! thanks again!
     

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