Question

What is the derivative of `f(x)=(e^(2x))(ln(x))`?

Answer 1

`f'(x)=e^(2x)(2lnx+1/x)`

Explanation:

The derivative of `lnx` is `1/x`
The derivative of `e^g(x)`is `e^g(x)*g'(x)`
The derivative of `h(x)*l(x)` is `h'(x)*l(x)+h(x)*l'(x)`

Then

`f'(x)=e^(2x)*2*lnx+e^(2x)*1/x`

`=e^(2x)(2lnx+1/x)`