How Do You Apply the Chain Rule to Differentiate \( y = xe^{-x^2} \)?

[physicsed]

[SOLVED] another chain rule: easy one

$$y=xe^{-x^2}$$

i have no i dea how to start.
$$f'= x^{x^2} or -2x^blah blah blah$$

just get me started and i'll promise you i will finish it myself

 

[Feldoh]

This is actually an application of the product rule, then the chain rule.

 

[duke_nemmerle]

$$y=xe^{-x^2}$$

i have no i dea how to start.
$$f'= x^{x^2} or -2x^blah blah blah$$

just get me started and i'll promise you i will finish it myself

You will probably want to use the product rule and the rule for finding the derivative of $$e^{g(x)}$$

 

[rocomath]

Product rule!

$$f(x)=e^{-x^2}$$

derivative of e is itself, times the derivative of it's exponent.

 

[rocomath]

wow 3 replies all at 22:49 ... you just got the royal treatment :D

 

[Feldoh]

wow 3 replies all at 22:49 ... you just got the royal treatment :D

ROFL

 

[Dick]

Start with the product rule. When you get to needing to find d/dx(e^(-x^2)) then remember the chain rule says (f(g(x)))'=f'(g(x))*g'(x). f is exp. g(x)=-x^2. So?

 

[physicsed]

Solved it
thanks

 

[Dick]

Geez. I'm really late.

 

[physicsed]

$$Y'= e^{-x2}(1-2x^{2})$$
thanks for the help

 

[Feldoh]

Looks right^^