Question

How do you differentiate `g(x) = e^(2x)ln3x` using the product rule?

Answer 1

I found: `e^(2x)[2ln(3x)+1/x]`

Explanation:

The Product Rule tells you that if you have:

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

In your case for each function you will need, when derived, to use also the Chain Rule (in red) to get:

`g'(x)=color(red)(2e^(2x))ln(3x)+e^(2x)color(red)(1/(3x)*3)=`

`=e^(2x)[2ln(3x)+1/x]`