Thinking Backwards Examples

What is a function whose derivative is 2xe^x2?

Rearrange this a little. 

 2xe^x2 = e^x2 · (2x). 

 If we let u = x², then u' = 2x and therefore e^x2 · (2x) = e^u · u' .

What function has a derivative of e^u · u'?

e^u. Our answer is e^u, or e^x2.