How do I differentiate e^-2x * y?

In summary, the conversation is about the differentiation of a product using Leibniz notation, specifically the expression d/dx ( f(x)y) = f'(x)y + f(x)dy/dx. One person expresses dislike for Leibniz notation, while the other defends its usefulness.
  • #1
James889
192
1
Hi,

I need to differentiate the following [tex]\frac{d}{dx}[e^{-2x}y][/tex]

Does the `dx` mean that the y turns into x?

I know i have to use the product rule.
 
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  • #2
Hi James889! :smile:

No, you just write "dy/dx" …

d/dx ( f(x)y) = f'(x)y + f(x)dy/dx :wink:
 
  • #3
tiny-tim said:
Hi James889! :smile:

No, you just write "dy/dx" …

d/dx ( f(x)y) = f'(x)y + f(x)dy/dx :wink:

Hm?, what do you mean `just write`?

I can't think of anyone i hate more than Wilhelm Leibniz, for coming up with this stupid notation :mad:
 
  • #4
James889 said:
Hm?, what do you mean `just write`?

I can't think of anyone i hate more than Wilhelm Leibniz, for coming up with this stupid notation :mad:

he he, get used to it! :biggrin:

(it's particularly useful when you start using substitution of variables in integals)

of course, you could write " y' " instead. :wink:
 
  • #5
James889 said:
I can't think of anyone i hate more than Wilhelm Leibniz, for coming up with this stupid notation :mad:
Personally, I prefer Leibniz notation over Newton's notation as being more informative. The notation dy/dx is lots more informative than, say y' inasmuch as the Leibniz notation tells you exactly which variable with which differentiation is with respect to.
 

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