Question

Question #efb97

Answer 1

`f'(x)=3e^(-(x^2/2))(1-x^2)`

Explanation:

Using the Product Rule with

`g(x)=3x` and `h(x)=e^(-(x^2/2))`

`f'(x)=g(x)h'(x)+g'(x)h(x)`

Find the derivatives, `g'(x)` and `h'(x)`
`g'(x)=3` and `h'(x)=-xe^(-(x^2/2))`

Plug this into the formula for the Product Rule
`f'(x)=3x(-xe^(-(x^2/2)))+3e^(-(x^2/2))`
`=3e^(-(x^2/2))(1-x^2)`