Question

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

Answer 1

`f'(x)=2x^2e^x`

Explanation:

The product rule states that
`d/dx[f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`.

Using this rule, together with other standard rules of differentiation yields

`d/dx(2x^2-4x+4)e^x=(2x^2-4x+4)e^x+(4x-4)e^x`

`=e^x(2x^2)`