How do you find derivative of xe^(x^2)

1. Apr 13, 2013

Lo.Lee.Ta.

1. This may seem like a dumb question, but I don't really know the steps of how to find this derivative...

f(x)= xex2

2. The answer is supposed to be: e-x2*(1-2x2)

I thought to do u-substitution.

u= x2

du= 2xdx

1/2du = xdx

(1/2)eudu

(1/2)ueu-1

(1/2)(x2)(ex2-1)

hhhh =_= How is the real answer supposed to be: e-x2(1-2x2)???

Thanks :)

2. Apr 13, 2013

Staff: Mentor

you need to apply the product rule y=uv dy/dx = du/dx * v + u * dv/dx

and for the dv/dx you need to use the dy/dx = e^u du/dx

There's also some confusion here: y = x * e ^ (x^2) or is it y = x * e ^ (-x^2)

Last edited: Apr 13, 2013
3. Apr 13, 2013

Lo.Lee.Ta.

The product rule for this would be:

(1)(ex2) + (x)(2xex2)

= ex2 + 2x2ex2

If I factor out ex2, I would get:

ex2(1 + 2x2)

Similar, but they have negatives! How is that? :?

4. Apr 13, 2013

Infrared

Is it possible that the problem was supposed to have $e^{-x^2}$? That is the only explanation I can see.

5. Apr 13, 2013

Lo.Lee.Ta.

Hey, you were right! I copied it down wrong! #O_O

It was xe-x2

e-x2(1-2x2)