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

[James889]

Hi,

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

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

I know i have to use the product rule.

 

[tiny-tim]

Hi James889!

No, you just write "dy/dx" …

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

 

[James889]

Hi James889!

No, you just write "dy/dx" …

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

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

 

[tiny-tim]

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

he he, get used to it!

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

of course, you could write " y' " instead.

 

[Mark44]

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

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.