differentiation chain rule help

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

1. fudgesweetsNew 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. ResourceFinder

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. fudgesweetsNew 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?

5. fudgesweetsNew commenter

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