Question

How do you differentiate `g(x) = xe^(2x)` using the product rule?

Answer 1

The result is (2x+1)e^(2x).

Explanation:

The rule says that `d/dx f(x)*g(x)=df(x)/dx*g(x)+f(x)*dg(x)/dx`.
In this case the two functions are `x` and `e^(2x)`.
Unfortunately the text call the product `g(x)` and this can create some confusion with my description of the product rule.

`(dxe^(2x))/dx = dx/dx *e^(2x)+x*d/dxe^(2x)`

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

`=(2x+1)e^(2x)`.