What Basic Derivative Rule Is Responsible For This?

  • Thread starter DocZaius
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  • #1
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If:

[tex]a(x)=b(x)-c(x)[/tex]

Then:

[tex]\frac{da}{dx}=\frac{db}{dx}-\frac{dc}{dx}[/tex]

Please note that the sum/difference rule is not directly invoked since it talks about a derivative of a sum/difference being equal to the sum/difference of the derivatives. It could very well be the basis for this logic, although I don't see it offhand. And of course, this is not a homework question. I came across this logic today and was surprised I could use it.
 
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  • #2
LCKurtz
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It certainly is the sum-difference rule. When you compute a'(x) on the left you are asking for (b(x) - c(x))' on the right, which, by the difference rule is b'(x) - a'(x).
 
  • #3
365
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Ah yes! Thank you. All I had to do was write "d(b-c)" instead of "da" and I would have seen it immediately.
 

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