Question

What are the critical points of `f(x) =e^x-x^2e^(x^2)`?

Answer 1

`f'(x) = e^x -2xe^(x^2) + e^x(2xe^(x^2))`

Explanation:

`(e^x)' = e^x`
`(e^u)' = e^u*u'`

`f(x) = e^x - x^2*e^(x^2)`

use the Product Rule `f'g + fg'` for `x^2*e^(x^2)`
`f'(x) = e^x - (2x)(e^(x^2))+(e^x)(2xe^(x^2))`
`f'(x) = e^x -2xe^(x^2) + e^x(2xe^(x^2))`