Can the du's be cancelled out in the derivative (dy/dx)?

  • Thread starter wajed
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In summary, the speaker cautions against cancelling out the du's in the equation (dy/dx) = (dy/du)(du/dx) because even though it may resemble an algebraic identity, it is not a legitimate practice. They explain that the derivatives dy/dx and du/dx are not the same as quotients, and separating them out can lead to incorrect information. The speaker also reminds the listener that the chain rule is a legitimate identity, but it should not be thought of as a quotient.
  • #1
wajed
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"
(dy/dx) = (dy/du)(du/dx)

Caution: Notice that if (dy/du) and (du/dx) were quotients rather than expressions for derivatives, we could cancel the du`s and make (5) into an identity. But we stree that du has not been defined as an entity, and consequently it is not legitimate to cancel the du`s. Nonetheless, the resemblance between (5) and an algebraic identity makes it easy to remember.
"

so, he`s saying that I can`t cancel out the du`s, because they are not quotients, but expressions for derivative..
but I think that they can be canceled out!? is that true?
and yes they are expressions for derivative, but also they are quotients..
and I understand that we need them, and it would be meaningless to cancel them..
its just that I think he`s giving me wrong information when he said that I "can`t cancel them out" because "they are expressions for derivatives"

Am I wrong?
 
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  • #2
That's the chain rule. It is a legitimate identity, but it is not quite as immediately obvious as some may think.
 
  • #3
You should not think of them as quotients.

The derivative dy/dx is the limit of quotients. That is *not* the same thing as being a quotient. In some cases identities can be remembered because things cancel as if it were legitimate to separate the dy and dx. You should *not* think that you can separate them out at this stage.
 

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