Question

How do you differentiate `y = e^(2x) ln x`?

Answer 1

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

Explanation:

To differentiate `y=e^(2x)lnx`, we use product rule according to which if `f(x)=g(x)xxh(x)`

`(df)/(dx)=g(x)xx(dh)/(dx)+(dg)/(dx)xxh(x)`

As such `(dy)/(dx)=(e^(2x)xx2xxlnx)+(e^(2x)xx1/x)`

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