Question

How do you differentiate `f(x)=(4e^x+1)(x^2-3)` using the product rule?

Answer 1

`f'(x) = 4e^x(x^2+2x-13) + 2x`

Explanation:

`f(x) = (4e^x+1)(x^2-3)`

Click here for details on the product rule.
`f'(x) = d/dx(4e^x + 1)(x^2-3) + (4e^x + 1)d/dx(x^2-3)`

`f'(x) = (4e^x)(x^2-3) + (4e^x + 1)(2x)`

To simplify, we'll expand and see if we can condense it later:
`f'(x) = 4 e^x x^2 - 12e^x + 8 x e^x + 2x`

`f'(x) = 4e^x(x^2+2x-13) + 2x`