Question

How do you differentiate `f(x)= (5+3x^2)*e^x` using the product rule?

Answer 1

`f'(x)=e^x(3x^2+6x+5)`

Explanation:

According to the product rule::

`f'(x)=e^xd/dx[5+3x^2]+(5+3x^2)d/dx[e^x]`

`f'(x)=6xe^x+5e^x+3x^2e^x`

`f'(x)=e^x(3x^2+6x+5)`